1/x squared - 25 minus x+5/x squared - 4x-5?

Question

shadowfiend · Answer

Eep. Could you use the equation editor here to write that out? It's not exactly clear what fractions go where and such.

anonymous · Answer

$$1/x ^{2}-25 - x +5/x ^{2}-4x -5$$

shadowfiend · Answer

Heh. Silly me. No fraction notation in the equation editor yet. This:

$$\frac{1}{x^2} - 25−x+\frac{5}{x^2}−4x−5$$

?

anonymous · Answer

well i dont know if it makes a difference but -25 is on the bottom of the left fraction next to x squared, then x + 5 all over x squared -4x - 5...... if that makes any sense

shadowfiend · Answer

Absolutely! Here we go:

$$\frac{1}{x^2 - 25} - \frac{x + 5}{x^2 - 4x - 5}$$

Look right? What do you want to find out about this?

shadowfiend · Answer

At a glance, the first thing that stands out is that $x^2 - 25$ is $(x + 5)(x - 5)$, part of which is the same as the top of the right fraction.

Also, if you factor the denominator of the right fraction, you get:

$$x^2 - 4x - 5 = (x - 5)(x + 1)$$

So now you have a common factor for the denominators as well. You should be able to do some interesting stuff once you write it out that way:

$$\frac{1}{(x + 5)(x - 5)} - \frac{x + 5}{(x - 5)(x + 1)}$$