x²/x-3=x+2/2x-5 rational equation solve

Multiply all terms by x and cancel:

x² + −3x = xx + xx + −5x

x² - 3x = 2x² − 5x (Simplify both sides of the equation)

x² − 3x − (2x² − 5x) = 2x² − 5x − (2x² - 5x) (Subtract 2x^2-5x from both sides)

−x²+ 2x = 0

x (−x + 2) = 0 (Factor left side of equation)

x = 0 or −x + 2 = 0 (Set factors equal to 0)

x = 0 or x = 2

Check answers. (Plug them in to make sure they work.)

x = 0 (Doesn't work in original equation)

x = 2 (Works in original equation)

The answer is