Question

How do you solve for p in `1/p+1/q=1/f`?

Answer 1

`color(blue)(p = (fq) / (q - f )`

Explanation:

`1/p + 1/q = 1/f`

Isolating the term containing `color(blue)(p)`
`1/color(blue)(p) + 1/q = 1/f`

`1/color(blue)(p) = 1/f - 1/q`

The L.C.M of the denominators of the terms on the L.H.S is `color(green)(fq`

`1/p = (1 * color(green)(q))/(f * color(green)(q)) - (1 * color(green)(f))/(q * color(green)(f))`

`1/p = q/(fq) - f/(fq)`

`1/p = (q - f ) /(fq)`

`color(blue)(p = (fq) / (q - f )`