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Hasil operasi aljabar  untuk  dan  adalah ...

Hasil operasi aljabar begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses end style untuk begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 5 x over denominator x plus 2 end fraction semicolon x not equal to negative 2 end style dan begin mathsize 14px style g open parentheses x close parentheses 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 space 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 space 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 space 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 space 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 space x not equal to negative 2 end style

Jawaban:

Perhatikan perhitungan berikut ini.

Ingat, selisih dua fungsi:

begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses equals f open parentheses x close parentheses minus g open parentheses x close parentheses end style

Maka:

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 open parentheses x close parentheses minus g open parentheses x close parentheses end cell row blank equals cell open parentheses fraction numerator 5 x over denominator x plus 2 end fraction close parentheses minus open parentheses 3 x minus 2 close parentheses end cell row blank equals cell fraction numerator 5 x over denominator x plus 2 end fraction minus fraction numerator open parentheses 3 x minus 2 close parentheses open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 5 x minus open parentheses 3 x minus 2 close parentheses open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 5 x minus open parentheses 3 x squared plus 6 x minus 2 x minus 4 close parentheses over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 5 x minus open parentheses 3 x squared plus 4 x minus 4 close parentheses 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

Perhatikan bahwa pada fungsi rasional begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator p open parentheses x close parentheses over denominator q open parentheses x close parentheses end fraction end style, penyebut begin mathsize 14px style q open parentheses x close parentheses not equal to 0 end style, maka nilai undefined membuat penyebut sama dengan begin mathsize 14px style 0 end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 end cell equals 0 row x equals cell negative 2 end cell end table end style

Didapatkan nilai begin mathsize 14px style x equals negative 2 end style membuat penyebut sama dengan begin mathsize 14px style 0 end style maka begin mathsize 14px style x not equal to negative 2 end style.

Jadi, rumus fungsi begin mathsize 14px style left parenthesis p minus q right parenthesis left parenthesis x right parenthesis end style adalah begin mathsize 14px style fraction numerator negative 3 x squared plus x plus 4 over denominator x plus 2 end fraction semicolon space x not equal to negative 2 end style.

Dengan demikian, jawaban yang tepat adalah D.

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