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Hasil operasi aljabar untuk dan adalah ....

Hasil operasi aljabar begin mathsize 14px style left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end style untuk begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 5 x over denominator x plus 2 end fraction semicolon space x not equal to 1 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 3 x minus 2 end style adalah ....

  1. begin mathsize 14px style fraction numerator 3 x squared minus x plus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2 end style 

  2. begin mathsize 14px style fraction numerator 3 x squared plus x minus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2 end style 

  3. begin mathsize 14px style fraction numerator negative 3 x squared minus x plus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2 end style 

  4. begin mathsize 14px style fraction numerator negative 3 x squared plus x plus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2 end style 

  5. begin mathsize 14px style fraction numerator negative 3 x squared minus x minus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2 end style 

Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f minus g close parentheses open parentheses x close parentheses end cell equals cell f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis end cell row blank equals cell fraction numerator 5 x over denominator x plus 2 end fraction minus left parenthesis 3 x minus 2 right parenthesis left parenthesis samakan space penyebut right parenthesis end cell row blank equals cell fraction numerator 5 x over denominator x plus 2 end fraction minus fraction numerator left parenthesis 3 x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 5 x over denominator x plus 2 end fraction minus fraction numerator 3 x squared plus 4 x minus 4 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 5 x minus 3 x squared minus 4 x plus 4 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator negative 3 x squared plus x plus 4 over denominator x plus 2 end fraction end cell end table end style
 

Hasil dari begin mathsize 14px style left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end style berupa pecahan, sehingga penyebut tidak boleh nol.
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 end cell not equal to 0 row x not equal to cell negative 2 end cell end table end style
 

Oleh karena itu, jawaban yang benar adalah D.
 

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