Question

How do you solve `4 / (x+1) + 3 / (x - 4) = 2 / (x +1)`?

Answer 1

`x=1`

Explanation:

The usual approach might be to multiply by the LCD to cancel the denominators. However two of the denominators are the same.
Put them together on one side.

`4 / (x+1) + 3 / (x - 4) = 2 / (x +1)`

`color(red)(4 / (x+1) - 2 / (x +1)) = - 3 / (x - 4)`

`(2)/(x+1) = 3/-(x-4)" "larr` one fraction each side, cross-multiply

`3(x+1) = -2(x-4)`

`3x+3 =-2x+8`

`3x+2x = 8-3`

`5x = 5`

`x =1`