Solve the rational equation. Check your solutions by checking the domain restriction. Show all work,

Question

2/x-5 - x+1/x+4 = 6/x²-x-20

Answer 1

2/(x-5) - (x+1)/(x+4) = 6/(x-5)(x+4)

multiply by LCD (x-5)(x-4)

2x+8 - (x-5)(x+1) = 6

2x -x^2 +4x +5-6+8 = 0

-x^2 +6x +7= 0

(x-7)(x+1) = 0

x = 7, -1

check the solutions

2/(-6) - 0 = 6/(-6)3

-1/3 =-1/3

2/(2) -8/11 = 6/2(11)

1-8/11 = 3/11

domain is all real numbers except 5 and -4