Question

simplify
(a^-1+b^-1)/(ab)^-1

Answer 1

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

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

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

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

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

ab gets cancelled

$= b + a$

Answer 2

Step-by-step explanation:

=

(ab)

−1

(a

−1

+b

−1

)

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

ab

1

a

1

+

b

1

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

ab

1

ab

b+a

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

ab

b+a

÷

ab

1

= \frac{b + a}{ab} {\times ab}=

ab

b+a

×ab

ab gets cancelled

= b + a=b+a