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Diketahui . Tentukan: a.

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:

a. begin mathsize 14px style p left parenthesis x right parenthesis space dan space q left parenthesis x right parenthesis comma end style 

Pembahasan Soal:

Menentukan undefined dari undefined.

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   

Menentukan 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 x t minus t end cell equals 2 row cell x t 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   

Jadi begin mathsize 14px style p left parenthesis x right parenthesis equals fraction numerator 7 x minus 2 over denominator 2 x minus 1 end fraction end style dan begin mathsize 14px style q left parenthesis x right parenthesis equals fraction numerator negative 3 x plus 4 over denominator x end fraction end style.  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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