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

1 Answer
Mar 22, 2018

x = 1.

Explanation:

First, multiply and divide the first fraction on the left by x-4 and the second fraction on the left by x+1 to make them comparable.

We get (4(x-4) + 3(x+1))/((x+1)(x-4)) = 2/(x+1).

After cancelling x+1 on both sides, we get,

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

On expanding the numerator and cross multiplying the denominator we get,

7x-13 = 2x-8

This gives us 5x = 5

And thus x = 1.