Question

Multiply the rational expression

Answer 1

Always try to factor in your first step if you can.

In the numerator of the first fraction, notice that we have

a greatest common factor of 4 so we have 4(3f - 4).

Now in the denominator of the second fraction, we have the difference

of two squares which can be factored as the product of two binomials.

So we have (3f + 4)(3f - 4) in the denominator.

So we now have 4(3f - 4)/16 · 5/(3f + 4)(3f - 4).

Now, cross-cancel.

Notice that the 3f - 4's cancel out completely.

Multiplying across the top and bottom, we get 20/16(3f + 4).

The 20 and 16 can reduce to 5 and 4.

So we have 5/4(3f + 4).

Answer 2

Simplify your work by factoring before multiplying.  We get:

4(3f-4)          5
---------- * -----------------
    16        (3f-4)(3f+4)

Cancel the (3f-4) terms, obtaining:

             20
------------------
       16 (3f+4)
                                    5
Reducing, we get -------------      and this is the desired result.
                               4(3f+4)