How do you solve the rational equation (x+2)/(x+1)-(x-4)/(x-3)=0x+2x+1x4x3=0?

1 Answer
Jun 8, 2018

x=1x=1

Explanation:

add [x-4]/[x-3]x4x3 to both sides

[x+2]/[x+1]=[x-4]/[x-3]x+2x+1=x4x3

multiply both sides by (x+1)(x-3)(x+1)(x3)

(x-3)(x+2)=(x-4)(x+1)(x3)(x+2)=(x4)(x+1)

x^2+2x-3x-6=x^2+x-4x-4x2+2x3x6=x2+x4x4

x^2-x-6=x^2-3x-4x2x6=x23x4

add x^2x2 to both sides

-x-6=-3x-4x6=3x4

add 3x3x to both sides

2x-6=-42x6=4

add 6 to both sides

2x=22x=2

divide by 2

x=1x=1