Hello, ( have to use decimals to seperate the fractions, with out them it jams it all together)

I am stuck on this.
It's simplify the following complex fraction: with a LCD
x-(1/x)
x+(1/x)
Need help, and place show all work, thanks.
I am getting 2x^2??

Solve the following linear equation: with a LCD
36 - ..1 = 1
X .....10.. 5
I got X = 120?

I think this one can not be solved
4x ...+.... 8 ......= 2
2x+1..... x+1
Is this abled to be factored at all?

Perfom the indicated operation and simplfy your answer:\ YOu have to find a LCD in this
3 +.... x -..... 7
ax ...2a^2.... 2x
I got
-7a^2 + 6a + x^2 / 2a^2x ??
Is this correct??

Thanks for your help and looking at this.
Jo

2. Is this what you're after?

$\frac{x-\frac{1}{x}}{x+\frac{1}{x}}$

$\frac{x^2-1}{x^2+1}$ (from multiplying top and bottom by x)

$\frac{(x^2+1)-2}{x^2+1}$

$\frac{x^2+1}{x^2+1}-\frac{2}{x^2+1}$

$1-\frac{2}{x^2+1}$

3. $x + \frac{1}{x} = \frac{x^{2} + 1}{x}$

$x - \frac{1}{x} = \frac{x^{2} - 1}{x}$

$\frac{\frac{x^{2} - 1}{x}}{\frac{x^{2} + 1}{x}} = \frac{x^{2} - 1}{x} \cdot \frac{x}{x^{2} + 1} = \frac{x^{2} - 1}{x^{2} + 1}$

I'd love to see how you get 2x^2 out of that. Please demonstrate.

4. The question is

x - 1
.....X
_________
x + 1
.....X

That is what I am asking, yours is different.
Your answer to the one above is different. So I am confused now.

5. It looks like TKHunny answered the question correctly:

$\frac{x-\frac{1}{x}}{x+\frac{1}{x}}$

$=\frac{\frac{x^{2} - 1}{x}}{\frac{x^{2} + 1}{x}}$

$=\frac{x^{2} - 1}{x^{2} + 1}$

I just rearranged it a bit more...

6. Bradycat, you simply must get your algebra up to speed. There are various ways to manipulate various things. If it doesn't look the same, MAKE IT looke the same, don't just punt. Of course, by "make it", I mean to use appropriate transformations and operations. You can't just start hacking.