Having trouble with this problem.

[littlebit53]

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]

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]

Corrected version in first post.

 

[stapel]

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

So the expression is as follows?

. . . . .(4x² - 9)/(4x²) + 12 + (9)/(6x - 9)

That is:

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

Please confirm or correct.

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

Thank you.

Eliz.

 

[littlebit53]

DIVDE:


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

 

[stapel]

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.