1. ## Algebraic Fraction

1 / x² + x + 1 / x² - x

I am unsure as to how this is done. Any help is greatly appreciated.

Thank you.

2. Originally Posted by stellina_91
1 / x² + x + 1 / x² - x

I am unsure as to how this is done. Any help is greatly appreciated.

Thank you.
Is it 1 / (x² + x) + 1 / x² - x or (1 / x²) + x + 1 / x² - x?

And what do you want to do with it. Integrate? Differentiate? Put under a common denominator? Paint red?

3. The first one please, I would like to simplify it.

4. Originally Posted by stellina_91
The first one please, I would like to simplify it.
$\frac{1}{x^2 + x} + \frac{1}{x^2 - x} = \frac{1}{x(x + 1)} + \frac{1}{x(x - 1)}$

so you should try to put over a common denominator of x(x+1)(x-1):

$= \frac{x - 1}{x(x + 1)(x-1)} + \frac{x+1}{x(x - 1)(x+1)}$

$= \frac{(x - 1) + (x + 1)}{x(x + 1)(x-1)}$

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

$= \frac{2}{(x + 1)(x-1)}, \, x \neq 0$

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

You can check this by plugging in a value or two of x and seeing that you get the same answer for each expression.

5. Thanks so much for your help! I understand completely