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2/(x-1)+ 5/(x+3) =? ...?

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)

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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)