# Math Help - Expression

1. ## Expression

Simplify the expression:

$\frac{1}{1-x}-\frac{1}{1+x}-\frac{1}{1+x^2}-\frac{1}{1+x^4}-\frac{1}{1+x^8}$

2. Originally Posted by Apprentice123
Simplify the expression:

$\frac{1}{1-x}-\frac{1}{1+x}-\frac{1}{1+x^2}-\frac{1}{1+x^4}-\frac{1}{1+x^8}$
Convert the fractions to their common denominator (surprising simple), and then combine the numerators (nasty!).

$\frac{(1+x)(1+x^2)(1+x^4)(1+x^8)}{1-x^{16}}-\frac{(1-x)(1+x^2)(1+x^4)(1+x^8)}{1-x^{16}}$

. . . $-\frac{(1-x^2)(1+x^4)(1+x^8)}{1-x^{16}}-\frac{(1-x^4)(1+x^8)}{1-x^{16}}-\frac{(1-x^8)}{1-x^{16}}$

...I think that's right....

3. Now, multiply each numerator and then combine all the like terms ...