The LCD is the product of (x -2)(x + 1)
To clear the fractions, multiply each term by the part of the LCD that the denominator is missing.
x(x + 1) + (x - 2)(x - 1) = -1(x - 2)(x + 1)
Distribute and foil, then combine like terms.
x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2
2x^2 - 2x + 2 = -x^2 + x + 2
add x^2 to both sides
3x^2 -2x + 2 = x + 2
subtract from both sides
3x^2 - 3x + 2 = 2
subtract 2 from both sides.
3x^2 - 3x = 0
Factor out the GCF
3x(x - 1) = 0
Set each factor equal to zero and solve.
3x = 0 x - 1 = 0
x = 0 x = 1
