Question

4(x^2 - 9)^2 - (x + 3)^2/x^2 + 6x + 9

Answer 1

Is the following the problem expression?\[\frac{4 \left(x^2-9\right)^2-(x+3)^2}{x^2+6 x+9} \]

Answer 2

Yes @robtobey

Answer 3

Multiply out the numerator.\[\frac{4 x^4-72 x^2+324-x^2+6 x+9}{x^2+6 x+9} \]\[\frac{4 x^4-72 x^2+324-x^2+6 x+9}{x^2+6 x+9}=\frac{4 x^4-72 x^2+324}{x^2+6 x+9}-\frac{x^2+6 x+9}{x^2+6 x+9}=\frac{4 x^4-72 x^2+324}{x^2+6 x+9}-1 \]\[\frac{4 x^4-72 x^2+324}{x^2+6 x+9}-1=\frac{\left(4 (x-3)^2 (x+3)^2\right)}{(x+3)^2}-1=\left(4 (x-3)^2 \right)-1=4 x^2-24 x+35 \]

Answer 4

Rob the answer is (2x - 7)(2x - 5)

Answer 5

I don't know how to derive it.

Answer 6

\[4 x^2-24 x+35=(2 x-7) (2 x-5) \]

Answer 7

I can't see what you type, Open study cut it off.

Answer 8

I need to fix this problem before I can see people's comments. /sigh

Answer 9

http://openstudy.com/study#/updates/4fc395dde4b0964abc86391e

Answer 10

The following\[4 x^2-24 x+35 \]can be factored to give the "answer"\[(2 x-7) (2 x-5) \]Did the above come through?

Answer 11

Yes

Answer 12

But I want to see the method you did for solving the problem but I can't because the side is cut off. Do you mind retyping it but in a way so it doesn't get cut off?

Answer 13

Hold on. I will attach a Mathematica PDF file.

Answer 14

@robtobey Are you still there?

Answer 15

Almost finished.

Answer 16

A Mathematica solution is attached.

Answer 17

You could also solve by division. Refer to the attachment.

Answer 18

Thank you!

Answer 19

You are welcome.