Question

How to solve rational equation:

Answer 1

Like when adding/subtracting fractions at any other time, you need a common denominator, in this case (x-1)(x+1)=x^2-1 so:

(2(x+1)+3(x-1))/(x^2-1)=4  multiply both sides by (x^2-1)

2x+2+3x-3=4x^2-4  combine like terms on left

5x-1=4x^2-4  subtract (5x-1) from both sides

4x^2-5x-3=0 using the quadratic formula for expediency

x=(5±√73)/8

x≈-0.443 and 1.693