Question

Simplify. (4x - 12)/(x^2 - 9) * (x+3)/(5x^2-25x) / (28)/(x^2-25)

Answer 1

I need to factor out like terms

Answer 2

also These are fractions.

Answer 3

Okay, so @Kaihalojr, what does \(4x - 12\) factor to?

Answer 4

@Hero it can factor to x - 3 right?

Answer 5

Yes, but what did you factor out in order to get \(x - 3\) as one of the factors?

Answer 6

4 because that's a number that they are both divisible by.

Answer 7

Okay, so wouldn't that make both \(4\) and \(x - 3\) factors of \(4(x - 3)\)?

Answer 8

Oops, wrote that wrong. Guess that's a freebee for you.

Answer 9

So yeah \(4x - 12\) factors to \(4(x - 3)\) since \(4(x - 3) = 4x - 12\)

Answer 10

so for the bottom half of the fraction isn't x² - 9 a difference of squares?

Answer 11

Correct and how would you write that in factored form?

Answer 12

x - 3

Answer 13

so this whole fraction is basically x - 3/x - 3

Answer 14

Is it?

Answer 15

wait no wouldn't it actually be 4(x-3)/(x-3)²?

Answer 16

Yes, but doesn't \(\dfrac{x - 3}{x - 3} = 1\)

And knowing that couldn't we just re-write \((4(x - 3))/(x - 3)^2\) as \(\dfrac{4}{x - 3} \cdot\ \dfrac{x - 3}{x - 3}\) and then as \(\dfrac{4}{x - 3} \cdot\ 1\)

Answer 17

I think so yes

Answer 18

Okay, so that should tell you what the first fraction should be

Answer 19

Any ideas on how to factor the second fraction?

Answer 20

I think the upper half doesn't need to be factored right? just the bottom?

Answer 21

Are you sure about that?

Answer 22

no that's why I'm asking you

Answer 23

Okay, so basically the denominators need to be factored out in this case.

Answer 24

Let's write it out

Answer 25

I'm thinking we divide 25 and 5 by 5 so it's 1 and 5 then we divide x^2 and x by x so it's x and 1 correct?

Answer 26

\(\dfrac{\dfrac{x + 3}{5x^2 -25x}}{\dfrac{28}{x^2 - 25}}\)

Answer 27

What can we factor from the denominator of the top fraction?

Answer 28

oh we can divide the whole thing by x right so it becomes 3/ 5x - 25?

Answer 29

What can we FACTOR from the denominator of the top fraction?

Answer 30

5 right because 5 and 25 can each be factored by 5 or x for x^2 and x

Answer 31

You can factor \(5x\) not \(5\) or \(x\).

Answer 32

oh yeah that makes sense so then it's x - 5 right?

Answer 33

Yes, and you know the denominator of the bottom fraction is difference of squares.

Answer 34

By the way, the first fraction is \(\dfrac{4}{x + 3}\)

Answer 35

which multiplied by (x+3)/(x-5) is now 4(x-3)/(x+3)(x-5) correct?

Answer 36

How do you figure that?

Answer 37

because after we factor the first two fractions that's the only idea that seems fitting plus with fraction number 3 the numerator is x^2 - 25 which if squared is x - 5 so both (x - 5)s can cancel out.

Answer 38

I say it's the only thing that fits because we must multiply

Answer 39

You should write out your steps one by one here. Using the draw tool

Answer 40

\(\dfrac{\dfrac{x + 3}{5x^2 -25x}}{\dfrac{28}{x^2 - 25}} = \)

Write what the above equals after factoring the denominators