# Math Help - need help with complex rational expression

1. ## need help with complex rational expression

1-2/3x
-----------(fraction line for readabilitys sake)
x-4/9x

first thing I do is get the common denominator which is 27x

I multiply it around and end up with:

27x - 18/27x^2-12

then I factor it and end up with

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

the answer is supposed to be

3/3x+2

can anyone help me? thanks!

2. Originally Posted by NecroWinter
9(3x-2)/3(9x^2-4)

the answer is supposed to be

3/3x+2

can anyone help me? thanks!

You need to learn the difference of two squares method.

$\displaystyle \frac{9(3x-2)}{3(9x^2-4)}= \frac{9(3x-2)}{3(3x-2)(3x+2)} = \frac{3}{3x+2}$

3. one more quick question only because my book doesnt explain things much

i have a problem that reads:
1/x+h - 1/x
---------------
h

the answer is 1/x(x+h)

im not sure how to find the common denominator with this one. i assume its x(x+h) but no matter which way i work it it just looks...wrong

4. $\displaystyle \frac{\frac{1}{x+h}-\frac{1}{x}}{h}= \frac{\frac{x-(x+h)}{x(x+h)}}{h}= \frac{1}{h}\times \frac{x-(x+h)}{x(x+h)} =\frac{1}{h}\times\frac{h}{x(x+h)}= \frac{1}{x(x+h)}$