Question

indices

(a^-1*b^-1)÷(a^-1+b^-1)
solve please​

Answer 1

Answer:

$\frac{a^{-1}b^{-1}}{a^{-1}+b^{-1}}=\frac{1}{b+a}$

Step-by-step explanation:

$\frac{a^{-1}b^{-1}}{a^{-1}+b^{-1}}$

$=\frac{a^{-1}b^{-1}}{\frac{1}{a}+\frac{1}{b}}$

$=\frac{a^{-1}b^{-1}}{\frac{b+a}{ab}}$

$=\frac{\frac{1}{ab}}{\frac{b+a}{ab}}$

$\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}$

$=\frac{1\cdot \:ab}{ab\left(b+a\right)}$

$=\frac{ab}{ab\left(b+a\right)}$

$\mathrm{Cancel\:the\:common\:factor:}\:a$

$=\frac{b}{b\left(b+a\right)}$

$\mathrm{Cancel\:the\:common\:factor:}\:b$

$=\frac{1}{b+a}$