A student was asked to simplify

2/(x-1) + 5/(x+3)

and gave the answer x= 2/7

Explain this student’s mistake.

---- I know the answer is x= -1/7 but I'm not sure how or where the student made the mistake? could someone walk threw the steps to solving this equation for me?

## Answers (2)

mulitply both sides by the common denominator (x-1)(x+3)

[2*(x-1)(x+3)]/[(x-1)] + [5*(x-1)(x+3)]/[(x+3)] = 0 then cancel terms and get

2*(x+3) + 5*(x-1) = 0 now distribute and get

2x + 5x + 6 - 5 =0 and combine like terms

7x +1 = 0 now subract the one from both sides

7x = -1 and divide by 7!!

x = -1/7

yay!

lcd = (x - 1)*(x + 3)

(2*(x + 3) + 5*(x - 1))/(x - 1)*(x + 3) =

(2*x + 6 + 5*x - 5)/(x - 1)*(x + 3) =

(7*x + 1)/(x - 1)*(x + 3)