Question

Simplify each radical expression. State any restriction on the variable.

Answer 1

\[\frac{ x^2 + 10x + 25 }{ x^2 + 9x + 20 }\]

Answer 2

This is a rational expression since rational expressions are fractions of polynomials.

Anyways, are you able to factor the top or bottom?

Answer 3

yes i think so

Answer 4

the top would be (x +5^2)

Answer 5

ok show me what you get when you factor each

Answer 6

close but no

Answer 7

The bottom would be (x + 5)(x + 4)

Answer 8

the top should be (x+5)^2 which is the same as (x+5)(x+5)

Answer 9

the bottom is correct

Answer 10

I'm not sure what to do next.

Answer 11

what terms do you notice in common between top and bottom?

Answer 12

the (x + 5)

Answer 13

those will cancel because they divide to 1

Answer 14

and because x*1 = 1*x = x

Answer 15

So it would just be (x + 5)/(x + 4)

Answer 16

Thanks!

Answer 17

yes

Answer 18

`State any restriction on the variable.`

Answer 19

Idk how to do that part..

Answer 20

hint: you cannot divide by zero

Answer 21

Would the restriction be how there was two (x + 5)?

Answer 22

what values of x make the denominator zero?

Answer 23

x + 4

Answer 24

(x+5)(x+4) = 0

x+5 = 0 or x+4 = 0

x = ??? or x = ???

Answer 25

neither it's not equal

Answer 26

if x+5 = 0, then what must x be?

Answer 27

-5

Answer 28

and if x+4 = 0 then x is what?

Answer 29

-4

Answer 30

so if either x = -5 or x = -4, then the entire denominator will be zero

therefore we have to exclude those values to avoid dividing by zero

Answer 31

(x+5)(x+4) = 0

x+5 = 0 or x+4 = 0

x = -5 or x = -4