Question

What is the solution set for `30/(x^2-9) - 5/(x-3) = 9/(x+3)`?

Answer 1

I found no real solution!

Explanation:

You can write it as:
`30/((x+3)(x-3))-5/(x-3)=9/(x+3)`
the common denominator can be: `(x+3)(x-3)`; so you get:
`(30-5(x+3))/((x+3)(x-3))=(9(x-3))/((x+3)(x-3))`
`(30-5(x+3))/cancel(((x+3)(x-3)))=(9(x-3))/cancel(((x+3)(x-3)))`
`30-5x-15=9x-27`
collect `x` on the left:
`-14x=-42`
`x=42/14=3`
BUT substituting `x=3` into the original equation you get a division by zero!!! We have no real solutions.