SMA

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

AdministratorMarch 2, 2022

0 192 Less than a minute

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. $\text{a+b}$
B. $\text{a-b}$
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.

$a^{-m}=\frac1{a^m}$ , $a\neq0$

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 $a-b$ .

Oleh karena itu, jawaban yang tepat adalah B.

AdministratorMarch 2, 2022

0 192 Less than a minute