Question

What is true about the solution of x^2/2x-6=9/6x-18?

Answer 1

x = ±√3

Explanation:

In order to avoid extraneous answers, I like to work these by transforming to an expression equal to zero.

`(x^2)/(2x-6)=(9)/(6x-18)\\\\(x^2)/(2(x-3))-(9)/(6(x-3))=0\\\\(x^2-3)/(2(x-3))=0\\\\x^2=3\\\\\boxed{x=\pm√(3)}`

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If you do this the usual way, by clearing fractions to start, you will get an extraneous solution of x=3.