Question

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

Answer 1

`(1)/(a(a-4))`

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

`(a)/((a-4)(a+4))` ×
`(a+4)/(a^2)`

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

`(1)/(a(a-4))`