Help with equation containing fractions

Question

I am stuck with this problem : 3/(x²—1) + 2x/(x+1) = 7x/(x—1) —1 

Answer 1

The first step is to multiply both sides by the LCD to clear all of the fractions.

 

The LCD is (x² - 1).

 

Multiply both sides by this and cancel the common factors in the denominators: x² - 1 = (x + 1)(x - 1).

 

3 + 2x(x - 1) = 7x(x + 1) - (x² - 1)

 

Multiply everything, collect like terms and move all terms to the right side:

 

3 + 2x² - 2x = 7x² + 7x - x² + 1

 

0 = 4x² + 9x - 2

 

This cannot be factored since b² - 4ac = 9² - 4(4)(-2) = 81 + 32 = 113 is NOT a perfect square. You will need the quadratic formula.

 

x = (-b ± √(b² - 4ac))/(2a) = (-9 ±√113)/8 = -9/8 ±(√113)/8.

 

Both answers need to be checked in the ORIGINAL equation. I recommend using a calculator to do this because the radical arithmetic will be quite messy. They should both check out.