Subtract. Then put into simplest form.?

Question

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

Answer 1

The denominators are the same, so you can simply subtract the numerators to form one fraction.

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

You can then factor the numerator because it is a difference of squares to form a new fraction, which you will be able to get rid of the denominator.

(x+3)(x-3)/(x-3)
x+3

It's important to note though that the domain will still be all reals except 3, because in the original equation you could not have 3 in the denominator. Even though x+3 is defined for all reals, the original equation was not, which is what you are rewriting.

Answer 2

common denominator means we can subtract the numerators.

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

x^2 - 9 factors into (x-3)(x+3)

so we have (x+3)(x-3)/(x-3)

The x-3 will cancel each other out.

Final answer is x+3