Question

Find the product. Simplify your answer. a/a^2-16 × a+4/a^2​

Answer 1

Answer:

$\frac{1}{a(a-4)}$

Step-by-step explanation:

Factor the denominator of the first fraction

a² - 16 ← is a difference of squares and factors as

a² - 16 = (a - 4)(a + 4), thus fraction becomes

$\frac{a}{(a-4)(a+4)}$ × $\frac{a+4}{a^2}$

Cancel the factor (a + 4) on numerator/denominator and the a and a², leaving

$\frac{1}{a(a-4)}$