Question

Simplify : (a-¹ + b-¹) ÷ (a-² - b-²)​

Answer 1

${\large{\boxed{\textsf{\textbf{~~~Given :-}}}}}$

It is given to simplify $\sf{( {a}^{ - 1} + {b}^{ - 1} ) + ( {a}^{ - 2} - {b}^{ - 2}) }$. .

${\large{\boxed{\textsf{\textbf{~~~Solution :-}}}}}$

$\sf{( {a}^{ - 1} + {b}^{ - 1} ) + ( {a}^{ - 2} - {b}^{ - 2}) }$

By removing parentheses. . .

$\bf \red{\to \: {a}^{ - 1} + {b}^{ - 1} + {a}^{ - 2} - {b}^{ - 2} }$

$\implies$ Hence, the value for $\sf{( {a}^{ - 1} + {b}^{ - 1} ) + ( {a}^{ - 2} - {b}^{ - 2}) }$, we get $\bf\blue{ \: {a}^{ - 1} + {b}^{ - 1} + {a}^{ - 2} - {b}^{ - 2} }$.