How do you solve #(x+2)/(x^2-6x-27)+(x-17)/(x^2-2x-63)=(x+1)/(x^2+10x+21)# and check for extraneous solutions?
Multiply everything by the least command denominator to remove the fractions The solve for x
The least common denominator for all three is
( x-9) x ( x+7) x (x +3)
multiply all the terms by the least common denominator
(x + 7) ( x+2) + (x+3)(x -7) = (x + 1) Multiplying this out gives
Use the quadratic equation to solve for the roots