Question

Simplify completely

Answer 1

\[\frac{ x^2-4x+4 }{ x^2+10x+25 }\times \frac{ x+5 }{ x^2+3x-10}\]

Answer 2

Have you factored the quadratics on both sides?

Answer 3

i dont know how

Answer 4

(x-2)(x-2)(x+5)
--------------------
(x+5)(x+5)(x+5)(x-2)

Answer 5

I factorized the top left numerator. (x-2)(x-2)

Answer 6

Now which "factors" cancel by division?

Answer 7

what do you mean?

Answer 8

When something appears both in the numerator (top) and in the denominator (bottom), they equal 1. We don't write the 1 when that happens.

Answer 9

the (x+5)?

Answer 10

Yes. One (x+5) disappears and one (x-2) disappears. They became 1s. When you multiply anything by 1, it is unchanged. This is why we don't write the 1 upon dividing.

Answer 11

So you are left with

(x-2)
----------
(x+5)(x+5)

You can write the bottom as

(x+5)^2 or x^2+10x+25

Answer 12

would the top be x-2 or (x-2)^2?

Answer 13

There is only one factor of (x-2)

Leave it alone.

Answer 14

The (^2) means there are TWO terms multiplied together.

For example:

2^2 = 2*2

Answer 15

Thanks!