Math CentralQuandaries & Queries


Question from Ayana, a student:

solve and check for extraneous solutions.

3x+6/ x²-4 = x+1/ x-2

x can not = {-2,2}

Hi Ayana,

On the left side there is a common factor in the numerator and the denominator can be factored as a difference of squares. Perform these factorizations and then cancel what you can. Solve the resulting equation for x.

Now you need to check that the result you obtained is actually a solution to the equation. First of all x can't be 2 or -2. If your solution is 2 or -2 then the original equation has no solution. If your solution is not 2 or -2 substitute it into the original equation to verify that it is a valid solution to the original equation.

I hope this helps,

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