# Having trouble with this problem.

#### littlebit53

##### New member
4x^2 - 9 / 4x^2 + 12 +9 ÷ (6x -9)

Actually the problem looks like 4x^2 -9 over 4x^2 + 12x +9 ÷ (6x -9)

#### stapel

##### Super Moderator
Staff member
You have posted:

. . . . .$$\displaystyle \L 4x^2\,-\,\frac{9}{4x^2}\,+\,12\,+\,\frac{9}{6x\,-\,9}$$

But what are the instructions for this? Are you supposed to simplify? Find the domain? Find the asymptotes? Graph? Or something else?

You say you are having trouble. Where? When you reply with the instructions, please include a clear listing of what you have done so far.

Thank you.

Eliz.

#### littlebit53

##### New member
Corrected version in first post.

#### stapel

##### Super Moderator
Staff member
littlebit53 said:
Actually the problem looks like 4x^2 -9 over 4x^2 + 12x +9 ÷ (6x -9)
So the expression is as follows?

. . . . .(4x<sup>2</sup> - 9)/(4x<sup>2</sup>) + 12 + (9)/(6x - 9)

That is:

. . . . .$$\displaystyle \L \frac{4x^2\, -\, 9}{4x^2}\, +\, 12\, +\, \frac{9}{6x\, -\, 9}$$

And you still need to provide the instructions, and show how far you got before you starting "having trouble".

Thank you.

Eliz.

#### littlebit53

##### New member
DIVDE:

4x^2 -9
-__________________ ÷ (6x -9)
4x^2 +12x +9

#### stapel

##### Super Moderator
Staff member
So the exercise is to simplify the following division:

. . . . .$$\displaystyle \L \frac{4x^2\, -\, 9}{4x^2\, +\, 12x\, +\, 9}\, \div\, (6x\, -\, 9)$$

A good way to start would be to convert the second expression into a fraction, and then invert and multiply:

. . . . .$$\displaystyle \L \left(\frac{4x^2\, -\, 9}{4x^2\, +\, 12x\, +\, 9}\right)\, \left(\frac{1}{6x\, -\, 9}\right)$$

Naturally the first step at this point would be the factor (such as 6x - 9 = 3(2x - 3), etc) and then cancel off any factors common to the numerator and denominator.

If you get stuck, please reply showing how far you have gotten.

Thank you.

Eliz.