Question

Can someone teach me how to do this? Thanks in advance! and Please hurry!

Simplify
2s^2 - 5s - 12 / 2s^2 - 9s + 4

Answer 1

take one part at a time, let's start with

2s^2 - 5s - 12

multiply the leading coefficient to the end term.

s^2 - 5s - 24

what two numbers multiply to give -24, but add to give -5?

Answer 2

-8 and 3

Answer 3

good job :)

Answer 4

Now we're going to factor s^2 -5s - 24 using -8 and 3

(s - 8)(s + 3)

with me so far?

Answer 5

Alright

Answer 6

now we're going to divide these factors by the leading coefficient we used to multiply them in order to get the factors

( s - 8/2)(s+3/2)

we're going to reduce these two factors as much as possible, and if we cant reduce them, we're going to take the denominator and multiply it to the variable. Like so

(s - 4)(2s + 3)

See what i did there?

Answer 7

Hmm, Where did the 2 in (2s + 3) come from?

Answer 8

we had (s + 3/2) and because we couldnt reduce it, the other simple form we could put it in was (2s + 3) by multiplying "2" to the "s"

Answer 9

Ok I understand

Answer 10

Awesome. Now the first part is simplified.

Answer 11

ok

Answer 12

Now can you work

2s^2 - 9s + 4 the same way we did the first one? I will guide you through it :)

Answer 13

Ok

Answer 14

So s^2 - 9s + 8
then -1 and -8
so (s - 1) and (s - 8)
am I doing ok so far?

Answer 15

you're doing absolutely fine :D

Now we're going to divide by the leading coefficient just like the last one. what would you get?

Answer 16

(2s - 1) and (s - 4)

Answer 17

yay!! you've got this!

Answer 18

haha

Answer 19

now we're going to put it all together.

2s^2 -5s - 12 = (s - 4)(2s + 3)
2s^2 - 9s + 4 = (s - 4)(2s - 1)

right?

Answer 20

ok, now we can get rid of both (s - 4) s right? making (2s + 3) over (2s - 1) right?

Answer 21

Yep :D You got it.

Answer 22

And you've got your answer ^_^

Answer 23

Yay! Thanks very much! Got time for one more problem?

Answer 24

I don't actually x_x heading down to dinner, haha xD

Answer 25

Ok thanks again have fun! Enjoy your dinner!

Answer 26

Thanks :D