Answer
$\frac{2}{(w + 3)(w - 4)}$
Work Step by Step
Let's factor the denominators first:
First denominator:
$w^2 - 4w - 21 = (w - 7)(w + 3)$
Second denominator:
We can split the middle term:
$5w^2 - 20w + 3w - 12$
Group the first two and last two terms:
$(5w^2 - 20w) + (3w - 12)$
Factor what is common out of the two groups:
$5w(w - 4) + 3(w - 4)$
Group the factors together:
$(5w + 3)(w - 4)$
Now, let's put the factored denominators back into the expression:
$\frac{5w + 3}{(w - 7)(w + 3)} • \frac{2w - 14}{(5w + 3)(w - 4)}$
Combine the two rational expressions into one by multiplying numerators together and denominators together:
$\frac{(5w + 3)(2w - 14)}{(w - 7)(w + 3)(5w + 3)(w - 4)}$
Now, we want to cancel out the factors that are common in the numerators and denominators of each rational expression:
$\frac{2w - 14}{(w - 7)(w + 3)(w - 4)}$
Factor out the common term in the numerator:
$\frac{2(w - 7)}{(w - 7)(w + 3)(w - 4)}$
Finally, we can cancel out the common factor in both the numerator and denominator:
$\frac{2}{(w + 3)(w - 4)}$
