Question

help! simplify the rational expression?

Answer 1

if someone could let me know how to start solving this that would be great!

Answer 2

just cant remember what to do first^

Answer 3

So with any rational expression, it's a good bet that we can cancel terms.
in order to do that, we need to try and factor wherever possible

Answer 4

So first, on top, can we factor x^2+4x-21?

Answer 5

yes i think..im not great at factoring! im actually quite bad at it.

Answer 6

7 and -3? so would that turn into (x+7) (x-3)

Answer 7

Right!

Answer 8

Now we do the same thing on bottom.
We'll have two factors (since the biggest power is 2)

Answer 9

Can you write your function out bigger please/ It's too tiny.

Answer 10

...and we need two numbers that multiply to get -42 and add up to 1 (for 1x in the middle)

Answer 11

is it \(\dfrac{x^2+4x-21}{x^2+x-42}\)?

Answer 12

hmm well it has to be 42 and 1 right?

Answer 13

what else adds up to be 1 but multiplies to 42? hahah

Answer 14

Jhanny, yes it is. it is a picture though, if you click on it it should come up bigger.

Answer 15

Can you think of two numbers that multiply to get 42 but are one away from each other?

Answer 16

i feel like it has to be simple but i cant think of anything

Answer 17

21 and 2 get 42 but wont equal 1..hmm

Answer 18

Need a hand?

Answer 19

yes sadly i think so hahah

Answer 20

6 and 7 :)

Answer 21

oh my gosh yup it was simple

Answer 22

and will it be x+7 and x-6 or x-7 and x+6

Answer 23

haha okay thank you. so now its (x+7) (x-3)/(x+7)(x-6)

Answer 24

ooh and then the x+7 cancels out

Answer 25

ah thank you so much! i may actually have some others, if i do i will tag you in them! i really appreciate the help!

Answer 26

And what do we have left?

Answer 27

(x-3)/(x-6) :)

Answer 28

or C^

Answer 29

Yes! That's right!And yw :)