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^2 -x -20)

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

multiply both sides by (x-5)(x+4) to eliminate fractions:

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

2x+8 -(x^2 -4x-5) = 6

-x^2 +6x -7=0

x^2 -6x +7=0

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

x= -1, 7

check x=-1

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

-1/3 + 0 = 6/(-2)(-3) = -1/3

check x =7

2/(7-5) -(7+1)/(7+4) = 6/(7-5)(7+4)

1 - = 6/(2)(11)

11/11 -8/11 = 3/11

11-8=3