Question

Using complete sentences, explain each step in simplifying the ratio x2+8x/x2+10x+16 and provide the simplified form.

Answer 1

Can you factor both the numerator and denominator?

Answer 2

im not sure how to do the denominator, but yes i know the numerator

Answer 3

Alright.
\[\frac{x^2 + 8x}{x^2 + 10x + 16} \implies \frac{x(x + 8)}{x^2 + 10x + 16}\]What are two factors of 16 that add up to 10?

Answer 4

8 & 2

Answer 5

Alright. Now place those factors as binomials.
\[\frac{x^2 + 8x}{x^2 + 10x + 16} \implies \frac{x(x + 8)}{(x + 8)(x + 10)}\]Do you see what to do now? Particularly something that can be cancelled?

Answer 6

yes, the (x+8) , which leaves you x/x+10

Answer 7

Yup. Good job!

Answer 8

thank you !

Answer 9

np :)