Question

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

Answer 1

Answer:

  x = ±√3

Step-by-step explanation:

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

  $\dfrac{x^2}{2x-6}=\dfrac{9}{6x-18}\\\\\dfrac{x^2}{2(x-3)}-\dfrac{9}{6(x-3)}=0\\\\\dfrac{x^2-3}{2(x-3)}=0\\\\x^2=3\\\\\boxed{x=\pm\sqrt{3}}$

__

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