Question

How do you evaluate `\frac { 4} { x } + \frac { 7} { x + 8} = 8`?

Answer 1

`x = (-53 pm sqrt 3833)/16`

Explanation:

`frac{4(x + 8) + 7x = 8x(x + 8)}{x(x + 8)}`

`4x + 32 + 7x = 8x^2 + 64x`

`0 = 8x^2 + 53x - 32`

`Delta = 53^2 + 4 * 8 * 32 = 3833`

`x = (-53 pm sqrt 3833)/16`