Solve for x:
5/(x + 1) = 3 - 4/(x - 1)
Bring 3 - 4/(x - 1) together using the common denominator x - 1:
5/(x + 1) = (3 x - 7)/(x - 1)
Cross multiply:
5 (x - 1) = (x + 1) (3 x - 7)
Expand out terms of the left hand side:
5 x - 5 = (x + 1) (3 x - 7)
Expand out terms of the right hand side:
5 x - 5 = 3 x^2 - 4 x - 7
Subtract 3 x^2 - 4 x - 7 from both sides:
-3 x^2 + 9 x + 2 = 0
Divide both sides by -3:
x^2 - 3 x - 2/3 = 0
Add 2/3 to both sides:
x^2 - 3 x = 2/3
Add 9/4 to both sides:
x^2 - 3 x + 9/4 = 35/12
Write the left hand side as a square:
(x - 3/2)^2 = 35/12
Take the square root of both sides:
x - 3/2 = sqrt(35/3)/2 or x - 3/2 = -sqrt(35/3)/2
Add 3/2 to both sides:
x = 3/2 + sqrt(35/3)/2 or x - 3/2 = -sqrt(35/3)/2
Add 3/2 to both sides:
Answer: | x = 3/2 + sqrt(35/3)/2 or x = 3/2 - sqrt(35/3)/2