SMA

Bentuk a−1+b−1ab−1−a−1b​ dapat disederhanakan menjadi ?

Bentuk fraction numerator text ab end text to the power of negative 1 end exponent minus text a end text to the power of negative 1 end exponent text b end text over denominator text a end text to the power of negative 1 end exponent plus text b end text to the power of negative 1 end exponent end fraction dapat disederhanakan menjadi …

A. text a+b end text
B. text a-b end text
C. fraction numerator 1 over denominator text a+b end text end fraction
D. fraction numerator text ab end text over denominator text a+b end text end fraction
E. fraction numerator text a+b end text over denominator text ab end text end fraction

Pembahasan

Sifat bilangan berpangkat di antaranya sebagai berikut.

a to the power of negative m end exponent equals 1 over a to the power of ma not equal to 0

Penyelesaian soal di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a b to the power of negative 1 end exponent minus a to the power of negative 1 end exponent b over denominator a to the power of negative 1 end exponent plus b to the power of negative 1 end exponent end fraction end cell equals cell fraction numerator a times begin display style 1 over b end style minus begin display style 1 over a end style times b over denominator begin display style 1 over a end style plus begin display style 1 over b end style end fraction end cell row blank equals cell fraction numerator begin display style a over b end style minus begin display style b over a end style over denominator begin display style 1 over a end style plus begin display style 1 over b end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator a squared minus b squared over denominator a b end fraction end style over denominator begin display style fraction numerator b plus a over denominator a b end fraction end style end fraction end cell row blank equals cell fraction numerator a squared minus b squared over denominator a b end fraction divided by fraction numerator b plus a over denominator a b end fraction end cell row blank equals cell fraction numerator a squared minus b squared over denominator up diagonal strike a b end strike end fraction cross times fraction numerator up diagonal strike a b end strike over denominator b plus a end fraction end cell row blank equals cell fraction numerator a squared minus b squared over denominator a plus b end fraction end cell row blank equals cell fraction numerator open parentheses a plus b close parentheses open parentheses a minus b close parentheses over denominator a plus b end fraction end cell row blank equals cell a minus b end cell end table

Berdasarkan uraian di atas, bentuk fraction numerator text ab end text to the power of negative 1 end exponent minus text a end text to the power of negative 1 end exponent text b end text over denominator text a end text to the power of negative 1 end exponent plus text b end text to the power of negative 1 end exponent end fraction dapat disederhanakan menjadi a minus b.

Oleh karena itu, jawaban yang tepat adalah B.

Related Articles

Leave a Reply

Your email address will not be published.

Back to top button