Question

Rectangle A has an area of 16 − x2. Rectangle B has an area of x2 + 2x − 24. In simplest form, what is the ratio of the area of Rectangle A to the area of Rectangle B? Show your work.

Answer 1

Ratio of A to B

(16-x^2)/(x^2+2x-24)

From here, factor the numerator and denominator

Answer 2

and cancel anything you can

Answer 3

?

Answer 4

What does 16-x^2 factor to?

Answer 5

um i dont know honestly :'(

Answer 6

16 - x^2

-x^2 + 16

-(x^2 - 16)

-(x^2 - 4^2)

-(x - 4)(x+4)

Answer 7

I'm taking advantage of the difference of squares rule

Answer 8

What do you get when you factor x^2+2x-24

Answer 9

um okkay?

Answer 10

? yah im stuck...i cant follow the same pattern as you just did cuz it longer...
:/ i think

Answer 11

x^2+2x-24 = (x-4)(x+6)

since -4+6 = 2 and -4*6 = -24

Answer 12

ohhhhhhhhhhhhhhhhh okkayyy

Answer 13

so

\[\Large \frac{16 - x^2}{x^2+2x-24}\]

becomes

\[\Large \frac{-(x - 4)(x+4)}{(x-4)(x+6)}\]

Answer 14

is that the simplest ratio? yes right?

Answer 15

no, you need to cancel and simplify

Answer 16

cancel what??

Answer 17

notice how there's a "x-4" in common

Answer 18

yes i do

Answer 19

they cancel

Answer 20

\[\Large \frac{-(x - 4)(x+4)}{(x-4)(x+6)}\]


\[\Large \frac{-\cancel{(x - 4)}(x+4)}{\cancel{(x - 4)}(x+6)}\]

Answer 21

but i tought they could only cancel if they were opposite? does the - sign include in that?

Answer 22

no, the - out front is a -1 out front

Answer 23

ok

Answer 24

which is a separate factor

Answer 25

so we're left with

\[\Large \frac{-(x+4)}{x+6}\]

\[\Large \frac{-x-4}{x+6}\]

Answer 26

so thats my anwser...

Answer 27

yes, that's your ratio

Answer 28

thank you so much! im like struggling in this module..:/

Answer 29

just keep at it and you'll get it eventually

Answer 30

@crististar