Question

Simplify . (1/c + 1/h)/(1/(c ^ 2) - 1/(r ^ 2))

Answer 1

`(\left(h+c\right)cr^2)/(h\left(r^2-c^2\right))`

Explanation:

`((1)/(c)+(1)/(h))/((1)/(c^2)-(1)/(r^2))`

Combine
`(1)/(c) + (1)/(h)`

`((h+c)/(ch))/((1)/(c^2)-(1)/(r^2))`

Combine the bottom, too.

`=((h+c)/(ch))/((r^2-c^2)/(c^2r^2))`

Apply the fraction rule

`=(\left(h+c\right)c^2r^2)/(ch\left(r^2-c^2\right))`

Cancel

`=(\left(h+c\right)cr^2)/(h\left(r^2-c^2\right))`

Therefore,
`(\left((1)/(c)+(1)/(h)\right))/(\left((1)/(\left(c^2\right))-(1)/(\left(r^2\right))\right)):\quad (\left(h+c\right)cr^2)/(h\left(r^2-c^2\right))`