Question

Please solve for x and state all x-values that are excluded from the solution set.

5/(x+1)+1/(x-3)=-6/(x^2-2x-3)

Answer 1

Factor x^2 - 2x - 3

5/x + 1 + 1/x - 3 = -6/(x - 3)(x + 1)

Multiply both sides by the Least Common Denominator (LCD): (x + 1)(x - 3)

5(x - 3) + x + 1 = -6

Simplify

6x - 14 = -6

Add 14 to both sides

6x = -6 + 14

Simplify -6 + 14 to 8

6x = 8

Divide both sides by 6

x = 8/6

Simplify 8/6 to 4/3

x = 4/3