Question

How do you simplify: x/x^2 - 9 subtracted by x/x + 3 then adding 3/ x - 3. I got common denominators than simplified. I ended with -x^2 + x + 9. Where did I go wrong?

Answer 1

what you got aginst standard math notation?

x/(x^2-9) - x/(x+3) + 3/(x-3)

once you get the common denominator of (x^2-9), the numerator is

x - x(x-3) + 3(x+3)
= x-x^2+3x+3x+9
= -x^2+7x+9

so the final fraction can be written as

-(x^2-7x-9)/(x^2-9)

Answer 2

x/(x^2 - 9) - x/(x + 3) + 3/(x - 3)

The common denominator is (x^2 - 9).
Note that x^2 - 9 = (x + 3)(x - 3). Rewriting,
= x/(x^2 - 9) - x(x - 3)/(x^2 - 9) + 3(x + 3)/(x^2 - 9)

Combine all the terms in the numerator,
= ( x - x(x - 3) + 3(x + 3) ) / (x^2 - 9)
= (x - x^2 + 3x + 3x + 9) / (x^2 - 9)
= (-x^2 + 7x + 9) / (x^2 - 9)

Hope this helps~ `u`