Question

Solve and check. ( 3 marks)

5/(x-1)+2/(x+1)=-6

Answer 1

5/(x-1) + 2/(x+1) = -6

LCD = (x-1)(x+1)

5(x+1)/(x-1)(x+1)+2(x-1)/(x+1)(x-1) =-6
(5x+5)/(x-1(x+1) + (2x-2)/(x+1)(x-1)=-6
Add the numerators:
(7x+3)/(x+1)(x-1) = -6
7x+3 = -6(x+1)(x-1)
7x+3 = -6(x^2-1)
7x+3 = -6x^2 + 6
6x^2 + 7x = 6 - 3 = 3
6x^2 + 7x - 3 = 0

Use AC method of factoring:
A*C = 6 * -3 = -18 = -2*9. Sum = B = 7.
6x^2 + (-2x+9x) - 3 = 0
(6x^2-2x) + (9x-3) = 0
2x(3x-1) + 3(3x-1) = 0
(3x-1)(2x+3) = 0

3x-1 = 0
3x = 1
X = 1/3

2x+3 = 0
2x = -3
X = -3/2

Solution set: X = -3/2, and 1/3.

Check:
5/(x-1) + 2/(x+1) = -6.
5/(-3/2-2/2) + 2/(-3/2+2/2) = -6
5/(-5/2) + 2/(-1/2) = -6
(-2) + (-4) = -6
-6 = -6

5/(1/3-3/3) + 2/(1/3+3/3) = -6
5/(-2/3) + 2/(4/3) = -6
-15/2 + 3/2 = -6
-12/2 = -6
-6 = -6