Question

Fan and Medal

Divide. Show all work. Make sure to simplify. Assume no denominator equals zero.

Answer 1

@aajugdar

Answer 2

factorize and show me ur work

Answer 3

I don't know how to factorize the numerator on the first one

Answer 4

You mean \[x ^{2}-144\]

Answer 5

Yass

Answer 6

Factoring a perfect square...144 is a perfect square. What is the square root of 144?

Answer 7

12

Answer 8

Factoring a perfect square...\[x ^{2}-C = (x+\sqrt{c}) \times (x-\sqrt{c})\]

Answer 9

So \[x^{2}- 144 =?\]

Answer 10

(x+12)(x-12), I think

Answer 11

Now factor the denominator

Answer 12

I don't think there's two numbers when multiplied give you 7, and when multiplied give you -60.

Answer 13

when added. sorry

Answer 14

Two numbers that are multiplied together to give you -60 and when ADDED to gether give you 7. So what two number do that?

Answer 15

12 and -5

Answer 16

(x-12)(x-5)

Answer 17

I mean (x+12)(x-5)

Answer 18

Ok now factor the other side of the equation and show me what we have.

Answer 19

Im not sure because 45 doesn't have a perfect square

Answer 20

It does not factor as a perfect square because x is not squared. What goes into both 9x and 45?

Answer 21

9

Answer 22

So the factor would be 9(x-5). And the factor for 3x-36 would be?

Answer 23

(x-6)(x+6)

Answer 24

There is no\[x ^{2}\]

Answer 25

6(x-6)

Answer 26

No try again.

Answer 27

What number goes into 3 and 36?

Answer 28

3(x-12)

Answer 29

Yes..So can you show me the factored equation now.

Answer 30

(x+12)(x-12) / (x+12)(x-5) divided by 3(x-12) / 9(x-5)
does it have to be simplified, or is already?

Answer 31

We have more to do..on the right side \[(x+12)(x+12) / (x+12)(x-5)\] How can you simplify this more?

Answer 32

wait isn't it (x+12)(x-12)

Answer 33

On both sides there is (x+12) do they cancel out?

Answer 34

Right. so now we have \[\frac{ (x-12) }{ (x-5) }\div \frac{ 3(x-12) }{ 9(x-5) }\]

Answer 35

No they do not cancel out.

Answer 36

That still isn't completely simplified?

Answer 37

Correct. How would you divide this?

Answer 38

Multiply?

Answer 39

the numerator by the denominator of the other side

Answer 40

You multiply but since we are dividing you have to invert the fraction on the right side then cross multiply. Example below.\[\frac{ 3 }{ 4 }\div \frac{ 2 }{ 3 } = \frac{ 3 }{ 4 } \times \frac{ 3 }{ 2 }\]

Answer 41

Then you cross multiply and simplify.

Answer 42

so basically (x-12)*9(x-5) and (x-5)* 3(x-12)

Answer 43

Yep..

Answer 44

What cancels out?

Answer 45

The only thing common is x

Answer 46

Are yu sure???\[\frac{ 9(x-12)(x-5) }{ 3(x-12)(x-5) }\]

Answer 47

And 3

Answer 48

So you answer is?

Answer 49

3(x-12)(x-5)

Answer 50

The (x-12) and (x-5) cancel out correct.