Question

If `p/q = r/s`, prove that `(2p + 3q)/(2p - 3q) = (2r + 3s)/(2r - 3s)`.

Answer 1

We have
`p/q = r/s`  ...[Multiplying both side by 2 / 3]
`(2p)/(3q) = (2r)/(3s)`   ...[By componendo and dividendo]
∴ `(2p + 3q)/(2p - 3q) = (2r + 3s)/(2r - 3s)`.
Hence proved.