Question

How do you solve `(x^2-x-6)/(x^2)=(x-6)/(2x)+(2x+12)/x`?

Answer 1

Put on a common denominator:

`(2(x^2 - x - 6))/(2x^2) =(x(x - 6))/(2x^2) + (2x(2x + 12))/(2x^2)`

`2x^2 - 2x - 12 = x^2 - 6x + 4x^2 + 24x`

`0 = 3x^2 + 20x + 12`

`0 = 3x^2 + 18x + 2x + 12`

`0 = 3x(x + 6) + 2(x + 6)`

`0 = (3x + 2)(x + 6)`

`x = -2/3 and -6`

Hopefully this helps!