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Diketahui . Tentukan: b. ,

Pertanyaan

Diketahui begin mathsize 14px style p open parentheses fraction numerator x plus 1 over denominator 2 x minus 1 end fraction close parentheses equals x plus 3 space dan space q open parentheses fraction numerator 2 over denominator x minus 1 end fraction close parentheses equals 2 x minus 5 end style. Tentukan:

b. begin mathsize 14px style open parentheses 3 p plus q close parentheses open parentheses 2 x plus 3 close parentheses end style

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 3 p plus q right parenthesis left parenthesis 2 x plus 3 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 p left parenthesis 2 x plus 3 right parenthesis plus q left parenthesis 2 x plus 3 right parenthesis end cell end table end style

Menentukan begin mathsize 14px style p open parentheses 2 x plus 3 close parentheses end style terlebih dahulu dengan mencari begin mathsize 14px style p open parentheses x close parentheses end style dari begin mathsize 14px style p open parentheses fraction numerator x plus 1 over denominator 2 x minus 1 end fraction close parentheses equals x plus 3 end style.  

Misal: begin mathsize 14px style s equals fraction numerator x plus 1 over denominator 2 x minus 1 end fraction end style maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row s equals cell fraction numerator x plus 1 over denominator 2 x minus 1 end fraction end cell row cell left parenthesis 2 x minus 1 right parenthesis s end cell equals cell x plus 1 end cell row cell 2 s x minus s end cell equals cell x plus 1 end cell row cell 2 s x minus x end cell equals cell 1 plus s end cell row cell left parenthesis 2 s minus 1 right parenthesis x end cell equals cell 1 plus s end cell row x equals cell fraction numerator 1 plus s over denominator 2 s minus 1 end fraction end cell row cell p left parenthesis s right parenthesis end cell equals cell open parentheses fraction numerator 1 plus s over denominator 2 s minus 1 end fraction close parentheses plus 3 end cell row blank equals cell open parentheses fraction numerator 1 plus s over denominator 2 s minus 1 end fraction close parentheses plus 3 open parentheses fraction numerator 2 s minus 1 over denominator 2 s minus 1 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 plus s over denominator 2 s minus 1 end fraction close parentheses plus open parentheses fraction numerator 6 s minus 3 over denominator 2 s minus 1 end fraction close parentheses end cell row blank equals cell fraction numerator s plus 6 s plus 1 minus 3 over denominator 2 s minus 1 end fraction end cell row blank equals cell fraction numerator 7 s minus 2 over denominator 2 s minus 1 end fraction end cell row cell p left parenthesis x right parenthesis end cell equals cell fraction numerator 7 x minus 2 over denominator 2 x minus 1 end fraction end cell end table end style   

Sekarang kita bisa menentukan begin mathsize 14px style p open parentheses 2 x plus 3 close parentheses end style dari begin mathsize 14px style p open parentheses x close parentheses equals fraction numerator 7 x minus 2 over denominator 2 x minus 1 end fraction end style dengan cara substitusi.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis x right parenthesis end cell equals cell fraction numerator 7 x minus 2 over denominator 2 x minus 1 end fraction end cell row cell p open parentheses 2 x plus 3 close parentheses end cell equals cell fraction numerator 7 open parentheses 2 x plus 3 close parentheses minus 2 over denominator 2 open parentheses 2 x plus 3 close parentheses minus 1 end fraction end cell row cell p left parenthesis 2 x plus 3 right parenthesis end cell equals cell fraction numerator 14 x plus 21 minus 2 over denominator 4 x plus 6 minus 1 end fraction end cell row cell p left parenthesis 2 x plus 3 right parenthesis end cell equals cell fraction numerator 14 x plus 19 over denominator 4 x plus 5 end fraction end cell end table end style 

Menentukan begin mathsize 14px style q left parenthesis 2 x plus 3 right parenthesis end style terlebih dahulu dengan mencari begin mathsize 14px style q open parentheses x close parentheses end style dari begin mathsize 14px style q open parentheses fraction numerator 2 over denominator x minus 1 end fraction close parentheses equals 2 x minus 5 end style.

Misal: begin mathsize 14px style t equals fraction numerator 2 over denominator x minus 1 end fraction end style maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row t equals cell fraction numerator 2 over denominator x minus 1 end fraction end cell row cell left parenthesis x minus 1 right parenthesis t end cell equals 2 row cell t x minus t end cell equals 2 row cell t x end cell equals cell 2 plus t end cell row x equals cell fraction numerator 2 plus t over denominator t end fraction end cell row cell q left parenthesis t right parenthesis end cell equals cell 2 open parentheses fraction numerator 2 plus t over denominator t end fraction close parentheses minus 5 end cell row blank equals cell open parentheses fraction numerator 4 plus 2 t over denominator t end fraction close parentheses minus 5 end cell row blank equals cell fraction numerator left parenthesis 4 plus 2 t right parenthesis minus 5 t over denominator t end fraction end cell row blank equals cell fraction numerator 2 t minus 5 t plus 4 over denominator t end fraction end cell row blank equals cell fraction numerator negative 3 t plus 4 over denominator t end fraction end cell row cell q left parenthesis x right parenthesis end cell equals cell fraction numerator negative 3 x plus 4 over denominator x end fraction end cell end table end style  

 Sekarang kita bisa menentukan begin mathsize 14px style q open parentheses 2 x plus 3 close parentheses end style dari begin mathsize 14px style q open parentheses x close parentheses equals fraction numerator negative 3 x plus 4 over denominator x end fraction end style dengan cara substitusi.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell q open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x plus 4 over denominator x end fraction end cell row cell q open parentheses 2 x plus 3 close parentheses end cell equals cell fraction numerator negative 3 open parentheses 2 x plus 3 close parentheses plus 4 over denominator open parentheses 2 x plus 3 close parentheses end fraction end cell row cell q open parentheses 2 x plus 3 close parentheses end cell equals cell fraction numerator negative 6 x minus 9 plus 4 over denominator 2 x plus 3 end fraction end cell row cell q open parentheses 2 x plus 3 close parentheses end cell equals cell fraction numerator negative 6 x minus 5 over denominator 2 x plus 3 end fraction end cell end table end style 

Pada soal, yang ditanyakan adalah menentukan begin mathsize 14px style open parentheses 3 p plus q close parentheses left parenthesis 2 x plus 3 right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 p plus q close parentheses open parentheses 2 x plus 3 close parentheses end cell equals cell 3 p open parentheses 2 x plus 3 close parentheses plus q open parentheses 2 x plus 3 close parentheses end cell row blank equals cell 3 open parentheses fraction numerator 14 x plus 19 over denominator 4 x plus 5 end fraction close parentheses plus open parentheses fraction numerator negative 6 x minus 5 over denominator 2 x plus 3 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 42 x plus 57 over denominator 4 x plus 5 end fraction close parentheses plus open parentheses fraction numerator negative 6 x minus 5 over denominator 2 x plus 3 end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses 42 x plus 57 close parentheses open parentheses 2 x plus 3 close parentheses plus open parentheses negative 6 x minus 5 close parentheses open parentheses 4 x plus 5 close parentheses over denominator open parentheses 4 x plus 5 close parentheses open parentheses 2 x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 84 x squared plus 126 x plus 114 x plus 171 close parentheses plus open parentheses negative 24 x squared minus 20 x minus 30 x minus 25 close parentheses over denominator open parentheses 8 x squared plus 12 x plus 10 x plus 15 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 84 x squared plus 240 x plus 171 close parentheses plus open parentheses negative 24 x squared minus 50 x minus 25 close parentheses over denominator open parentheses 8 x squared plus 22 x plus 15 close parentheses end fraction end cell row blank equals cell fraction numerator 84 x squared minus 24 x squared plus 240 x minus 50 x plus 171 minus 25 over denominator 8 x squared plus 22 x plus 15 end fraction end cell row blank equals cell fraction numerator 60 x squared plus 190 x plus 146 over denominator 8 x squared plus 22 x plus 15 end fraction end cell end table end style 

Jadi, begin mathsize 14px style left parenthesis 3 p plus q right parenthesis left parenthesis 2 x plus 3 right parenthesis equals fraction numerator 60 x squared plus 190 x plus 146 over denominator 8 x squared plus 22 x plus 15 end fraction end style

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