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Sederhanakan bentuk-bentuk aljabar berikut !

10.   begin mathsize 14px style fraction numerator begin display style fraction numerator x squared plus y squared over denominator x plus y end fraction end style over denominator begin display style x over y end style plus begin display style y over x end style end fraction end style         

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

bentuk sederhana dari begin mathsize 14px style fraction numerator begin display style fraction numerator x squared plus y squared over denominator x plus y end fraction end style over denominator begin display style x over y end style plus begin display style y over x end style end fraction end style adalah fraction numerator x y over denominator x plus y end fraction.

Pembahasan

Untuk menyelesaikan aljabar tersebut, sederhanakanlah dari pecahan terkecil.

fraction numerator begin display style fraction numerator x squared plus y squared over denominator x plus y end fraction end style over denominator begin display style x over y end style plus begin display style y over x end style end fraction equals fraction numerator begin display style fraction numerator x squared plus y squared over denominator x plus y end fraction end style over denominator begin display style fraction numerator x squared plus y squared over denominator x y end fraction end style end fraction space space space space space space space space space space space space space space space space equals fraction numerator x squared plus y squared over denominator x plus y end fraction cross times space fraction numerator x y over denominator x squared plus y squared end fraction space space space space space space space space space space space space space space space space equals fraction numerator x y over denominator x plus y end fraction

Dengan demikian, bentuk sederhana dari begin mathsize 14px style fraction numerator begin display style fraction numerator x squared plus y squared over denominator x plus y end fraction end style over denominator begin display style x over y end style plus begin display style y over x end style end fraction end style adalah fraction numerator x y over denominator x plus y end fraction.

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