Question

Simplify this equation! :) Please!

Answer 1

This works the same as the previous question. Factor the numerator and denominator, then simplify by cancelling factors of one.

Answer 2

Im sorry im stuck on the factoring part :? what would it look like?

Answer 3

???

Answer 4

Factoring isn't easy to explain. It's one of those things where either you know how to do it or you don't.

Answer 5

so what would the numerator and the denominator look like factored? :)

Answer 6

You're asking the wrong question. Your question should be, "Can you help me learn how to factor?".

Answer 7

the numerator would be 4(y+3)(y-3) right?

Answer 8

or am i way off?

Answer 9

If you multiplied that back out you would get something different

Keep in mind the numerator is a difference of squares. Difference of squares is always of the form \(a^2 - b^2\) = (a + b)(a - b)

So \(4y^2 - 9\) = (2y + 3)(2y - 3)

Answer 10

To factor the denominator, you must realize that a = 2, b = 1, c = -3

So you have to find two numbers x and y that multiply to get ac, but add to get b:

It would look something like this in general

x + y = b
xy = ac

In this case we already know what a, b, and c is so:

x + y = 1
xy = -6

So find two numbers that add to get 1, but multiply to get -6.

Answer 11

-3 and 2

Answer 12

You have it backwards. Its 3 and -2 because

3 - 2 = 1
3(-2) = -6

Answer 13

But good attempt either way

Answer 14

Now that we have that, the next thing to do is to split b, the middle term into two factors:

\(2y^2 + y - 3\) can be re-written as:

\(2y^2 + 3y - 2y - 3\)

Afterwards you:
Factor what's common to the first two terms: y
Factor what's common to the last two terms: -1

To get:

\(y(2y + 3) -1(2y + 3)\)

Lastly you extract the remaining common term which is 2y + 3 to get:
(2y + 3)(y - 1)

Answer 15

Now that we have the correct factored terms, we can re-write the fraction:

\[\frac{(2y+3)(2y - 3)}{(2y+3)(y - 1)}\]

Now you can cancel factors of one to simplify

Answer 16

Thanks!