SOLUTION: Add or subtract as indicated. Express the results in simplest form. (x^2)/(x- 3)- (9)/(x- 3)

Algebra ->  Expressions-with-variables -> SOLUTION: Add or subtract as indicated. Express the results in simplest form. (x^2)/(x- 3)- (9)/(x- 3)       Log On


   

Question 107235: Add or subtract as indicated. Express the results in simplest form.


(x^2)/(x- 3)- (9)/(x- 3)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%28x%5E2%29%2F%28x-+3%29-+%289%29%2F%28x-+3%29
.
Since the two fractions have the same denominator, their numerators can be combined
over the common denominator. The result is:
.
%28x%5E2+-+9%29%2F%28x-3%29
.
But the numerator is the difference of two squares. Therefore it can be factored according
to the following form:
.
A%5E2+-+B%5E2+=+%28A+%2B+B%29%2A%28A+-+B%29
.
In this case A = x and B = 3. So applying this factoring rule, we transform the problem to:
.

.
After the above cancellation of the term in the numerator that is common with the term in
the denominator, the equivalent value of original expression is reduced to x%2B3.
.
So the answer to this problem is x%2B3 is the simplest form of the given problem.
.
Hope this helps you to understand the problem.
.