Roboguru

Diketahui . Tentukan: d. .

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:

d. begin mathsize 14px style open parentheses q minus 2 p close parentheses open parentheses negative 2 close parentheses end style

Pembahasan Soal:

begin mathsize 14px style left parenthesis q minus 2 p right parenthesis left parenthesis negative 2 right parenthesis equals q left parenthesis negative 2 right parenthesis minus 2 p left parenthesis negative 2 right parenthesis end style 

Kita akan mencari nilai begin mathsize 14px style q open parentheses negative 2 close parentheses end style, maka kita misalkan begin mathsize 14px style fraction numerator 2 over denominator x minus 1 end fraction equals negative 2 end style.

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

Dari perhitungan tersebut didapat begin mathsize 14px style x equals 0 end style.

Diketahui bahwa 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, sehingga begin mathsize 14px style q left parenthesis negative 2 right parenthesis equals 2 left parenthesis 0 right parenthesis minus 5 equals negative 5 end style.

Kita akan mencari begin mathsize 14px style p open parentheses negative 2 close parentheses end style, maka kita misalkan begin mathsize 14px style fraction numerator x plus 1 over denominator 2 x minus 1 end fraction equals negative 2 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x plus 1 over denominator 2 x minus 1 end fraction end cell equals cell negative 2 end cell row cell x plus 1 end cell equals cell negative 2 left parenthesis 2 x minus 1 right parenthesis end cell row cell x plus 1 end cell equals cell negative 4 x plus 2 end cell row cell x plus 4 x end cell equals cell 2 minus 1 end cell row cell 5 x end cell equals 1 row x equals cell 1 fifth end cell end table end style  

Dari perhitungan tersebut didapat begin mathsize 14px style x equals 1 fifth end style.

Diketahui bahwa 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, sehingga

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis negative 2 right parenthesis end cell equals cell 1 fifth plus 3 end cell row blank equals cell fraction numerator 1 plus 3 left parenthesis 5 right parenthesis over denominator 5 end fraction end cell row blank equals cell fraction numerator 1 plus 15 over denominator 5 end fraction end cell row blank equals cell 16 over 5 end cell end table end style .

Jadi,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell q left parenthesis negative 2 right parenthesis minus 2 p left parenthesis negative 2 right parenthesis end cell equals cell negative 5 minus 2 open parentheses 16 over 5 close parentheses end cell row blank equals cell negative 5 minus 32 over 5 end cell row blank equals cell fraction numerator negative 5 left parenthesis 5 right parenthesis minus 32 over denominator 5 end fraction end cell row blank equals cell fraction numerator negative 25 minus 32 over denominator 5 end fraction end cell row blank equals cell negative 57 over 5 end cell end table end style   

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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