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Sederhanakan bentuk aljabar berikut ini.

fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style minus begin display style fraction numerator 2 over denominator x minus y end fraction end style over denominator begin display style fraction numerator 3 over denominator x minus y end fraction end style plus begin display style fraction numerator 4 over denominator x plus y end fraction end style end fraction 

L. Indah

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

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Jawaban

bentuk sederhana dari fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style minus begin display style fraction numerator 2 over denominator x minus y end fraction end style over denominator begin display style fraction numerator 3 over denominator x minus y end fraction end style plus begin display style fraction numerator 4 over denominator x plus y end fraction end style end fraction adalah fraction numerator negative x minus 3 y over denominator 7 x minus y end fraction .

Pembahasan

Langkah pertama untuk menyederhanakannya yaitu dengan menyamakan penyebutnya kemudian operasikan sesuai tanda pada soal.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style minus begin display style fraction numerator 2 over denominator x minus y end fraction end style over denominator begin display style fraction numerator 3 over denominator x minus y end fraction end style plus begin display style fraction numerator 4 over denominator x plus y end fraction end style end fraction end cell equals cell fraction numerator 1 left parenthesis x minus y right parenthesis minus 2 left parenthesis x plus y right parenthesis over denominator left parenthesis x plus y right parenthesis left parenthesis x minus y right parenthesis end fraction divided by fraction numerator 3 left parenthesis x plus y right parenthesis plus 4 left parenthesis x minus y right parenthesis over denominator left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis end fraction end cell row blank equals cell fraction numerator x minus y minus 2 x minus 2 y over denominator up diagonal strike left parenthesis x plus y right parenthesis left parenthesis x minus y right parenthesis end strike end fraction cross times fraction numerator up diagonal strike left parenthesis x plus y right parenthesis left parenthesis x minus y right parenthesis end strike over denominator 3 x plus 3 y plus 4 x minus 4 y end fraction end cell row blank equals cell fraction numerator negative x minus 3 y over denominator 7 x minus y end fraction end cell end table 

Dengan demikian, bentuk sederhana dari fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style minus begin display style fraction numerator 2 over denominator x minus y end fraction end style over denominator begin display style fraction numerator 3 over denominator x minus y end fraction end style plus begin display style fraction numerator 4 over denominator x plus y end fraction end style end fraction adalah fraction numerator negative x minus 3 y over denominator 7 x minus y end fraction .

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Sederhanakan bentuk-bentuk aljabar berikut ! 9.   3zx2y3​÷618xy​

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