Pertanyaan

Bentuk yang sederhana dari a 2 1 + b 2 1 a − 1 − b − 1 adalah...

Bentuk yang sederhana dari $\frac{a ^{- 1} - b ^{- 1}}{a ^{\frac{1}{2}} + b ^{\frac{1}{2}}}$ adalah...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

bentuk sederhana dari adalah .

bentuk sederhana dari $fraction numerator a to the power of negative 1 end exponent minus b to the power of negative 1 end exponent over denominator a to the power of begin display style 1 half end style end exponent plus b to the power of begin display style 1 half end style end exponent end fraction$ adalah $fraction numerator square root of b minus square root of a over denominator a b end fraction$ .

Pembahasan

Jadi, bentuk sederhana dari adalah .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator a to the power of negative 1 end exponent minus b to the power of negative 1 end exponent over denominator a to the power of begin display style 1 half end style end exponent plus b to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator begin display style 1 over a end style minus begin display style 1 over b end style over denominator square root of a plus square root of b end fraction end cell row blank equals cell fraction numerator begin display style 1 over a minus 1 over b end style over denominator square root of a plus square root of b end fraction cross times fraction numerator begin display style square root of a minus square root of b end style over denominator square root of a minus square root of b end fraction end cell row blank equals cell fraction numerator 1 over a square root of a minus 1 over a square root of b minus 1 over b square root of a plus 1 over b square root of b over denominator a minus b end fraction end cell row blank equals cell fraction numerator left parenthesis begin display style 1 over a end style minus begin display style 1 over b end style right parenthesis square root of a plus left parenthesis begin display style 1 over b end style minus begin display style 1 over a end style right parenthesis square root of b over denominator a minus b end fraction end cell row blank equals cell fraction numerator left parenthesis begin display style fraction numerator b minus a over denominator a b end fraction end style right parenthesis square root of a plus left parenthesis begin display style fraction numerator a minus b over denominator a b end fraction end style right parenthesis square root of b over denominator a minus b end fraction end cell row blank equals cell fraction numerator negative left parenthesis begin display style fraction numerator a minus b over denominator a b end fraction end style right parenthesis square root of a plus left parenthesis begin display style fraction numerator a minus b over denominator a b end fraction end style right parenthesis square root of b over denominator a minus b end fraction end cell row blank equals cell fraction numerator left parenthesis fraction numerator a minus b over denominator a b end fraction right parenthesis space left parenthesis negative square root of a plus square root of b right parenthesis over denominator a minus b end fraction end cell row blank equals cell left parenthesis fraction numerator a minus b over denominator a b end fraction right parenthesis space left parenthesis negative square root of a plus square root of b right parenthesis cross times fraction numerator 1 over denominator a minus b end fraction end cell row blank equals cell fraction numerator negative square root of a plus square root of b over denominator a b end fraction end cell row blank equals cell fraction numerator square root of b minus square root of a over denominator a b end fraction end cell row blank blank blank end table$

Jadi, bentuk sederhana dari $fraction numerator a to the power of negative 1 end exponent minus b to the power of negative 1 end exponent over denominator a to the power of begin display style 1 half end style end exponent plus b to the power of begin display style 1 half end style end exponent end fraction$ adalah $fraction numerator square root of b minus square root of a over denominator a b end fraction$ .

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