Question

What is the solution set for `(x-2)/(x+4)=2-(4/x)`?

Answer 1

I found:
`x_1=-8`
`x_2=2`

Explanation:

We can use as common denominator: `x(x+4)` to get:
`(x(x-2))/(x(x+4))=(2x(x+4)-4(x+4))/(x(x+4))`
We can cancel out both denominators and multiply:
`x^2-2x=2x^2+8x-4x-16` rearranging:
`x^2+6x-16=0`
We use the Quadratic Formula:
`x_(1,2)=(-6+-sqrt(36+64))/2=`
`x_(1,2)=(-6+-10)/2=`
So:
`x_1=-8`
`x_2=2`