Question

What is the simplified form of 4y^2-9 / 2y^2+y-3

Answer 1

4y^2-9 = (2y)^2 - 3^2
Use the identity \(a^2-b^2 = (a-b)(a+b)\) to factorize it.

2y^2 + y - 3
Split the middle term to make the factorization easier.
= 2y^2 (- 2y + 3y) - 3
Factorize the first two and the last two terms respectively by taking out the common factors of terms. Can you do the above work first?

Answer 2

Factorize the denominator, it's in the form ax^2 + bx + c

Answer 3

can you show me how to factor the denominator, i just get stuck on that- I know the numerator

Answer 4

So far, do you understand the step up to ''= 2y^2 (- 2y + 3y) - 3''?

Answer 5

Yeah and i think i just did it ... would 2y+3 / y+1

Answer 6

You can just use the cuadratic equation
\[x = \frac{-b \pm \sqrt(b^2 -4ac)}{2a}\]
I'd show you how in an easier way but I have to run to college

Answer 7

with the restrction of y doesnt equal 3/2 and -1

Answer 8

@kakrazz Not quite true, I mean the answer you get.

Answer 9

ugh so the answer is wrong??

Answer 10

What do you get for 2y^2 + y - 3 ? The factors, I mean.

Answer 11

when i split the middle term, i do 2y^2 (-2y + 3y) - 3... but how would i factor that?

Answer 12

how does that make it simpler?

Answer 13

2y^2 + (-2y + 3y) - 3
^
What are the common factors of the first two terms?

Answer 14

the common factor of 2y^2 and -2y is 2...

Answer 15

2y*

Answer 16

Yes. So, take that out and group the rest for the first two terms, that is
2y^2 - 2y = 2y (y-1)
Got it so far?

Answer 17

yes but what do I do with the 3y and -3... OH WAIT DO I FACTOR BY GROUPING? omg im sorry! I know that now!

Answer 18

i got it now! thank you @RolyPoly !!!!!

Answer 19

Glad that you know it!
What do you get for 2y^2 +y - 3 now?

Answer 20

i get (2y+3)(y-1) and the (2y+3) will cancel out and the final denominator will be y-1 !!

Answer 21

Yup!

Answer 22

THANK YOU!!!!

Answer 23

Welcome! Make sure you know that NEITHER 2x+3 nor y-1 is equal to 0!

Answer 24

YES! Thank you so so so so much!

Answer 25

Welcome!