2. Solve the rational equation x+3/x-2 = x+4/ x-5. What is the LCD? What are the domain restrictions? What are the solutions?

Answer 1

Given: (x+3) / (x-2) = (x+4) / (x-5)

Find: LCD, Domain restrictions, solution

Solution:

LCD = (x-2)*(x-5)

Domain: x NOT = 2, 5

Solve it:

(x+3) / (x-2) = (x+4) / (x-5) Just cross multiply

(x+3)*(x-5) = (x-2)*(x+4)

x^2 - 5x + 3x - 15 = x^2 + 4x - 2x - 8

-2x - 15 = 2x - 8

-7 = 4x

-7/4 = x