Question

((x)/(2x-6))-((3)/(x^2-6x+9))=((x-2)/(3x-9))
I need to show steps

Answer 1

How far have you gotten in this problem so far?

Answer 2

i've tried so many different ways and it seems like i just can get a logical answer

Answer 3

i don't know where to start really

Answer 4

We can make some headway with factoring the denominators of each term on each side a bit. :) This will help us obtain common denominators, then we only have to solve for the numerators being equal. (Making sure that our solution doesn't ultimately result in 1 / 0).

Answer 5

i just multiplied 3x-9 on the rhs, and on the lhs to start with

Answer 6

\[\frac{x}{2 x-6}-\frac{3}{x^2-6 x+9}=\frac{x-2}{3 x-9} \]\[\frac{x^2-3 x-6}{2 (x-3)^2}-\frac{x-2}{3 x-9}=0 \]\[\frac{x^2+x-30}{6 (x-3)^2}=0 \x^2+x-30=0

Answer 7

I mean starting with something as simple as...
\[\frac{x}{2x-6} = \frac{1}{2}\frac{x}{x-3}\]

Answer 8

And then

\[\frac{3}{x^2-6 x+9} = \frac{3}{(x-3)(x-3)}=\frac{3}{(x-3)^2}\]

Answer 9

And now we can see that the two terms on the left have (x-3) as a common factor.

Answer 10

\[\frac{x^2+x-30}{6 (x-3)^2}=0 \]\[x^2+x-30=0 \]\[\{x=-6\},\{x=5\} \]