Questions

Find a: $\rm \frac{a}{x-y} - \frac{x+y}{x^2 - y^2} = 0$

Prove: $\rm \frac{a^3}{a-1} + \frac{a^3}{a + 1} - \frac{2}{1 - a^2} = 2(a^2 + 1)$

Prove: $\rm \frac{3a-1}{a^2 - 1} + \frac{3a}{1 - a^2} + \frac{a}{1 + a^3} = \frac{1}{(1 - a)(1 + a^3)}$

Prove: $\rm \frac{2x}{x^2 - 1} - \frac{2x}{x^2 + 1} - \frac{4x}{x^4 + 1} = \frac{8x}{x^8 - 1}$

Prove: $\rm \frac{x - 3y}{x^2 - y^2} - \frac{3y}{y^2 - x^2} + \frac{xy}{x^3 + y^3} = \frac{x^3}{(x-y)(x^3 + y^3)}$

Prove: $\rm \frac{2}{1 - x^2} - \frac{2}{1 + x^2} + \frac{4}{1-x^4} = \frac{4}{1-x^2}$

Prove: $\rm \frac{2}{a^2 - 1} - \frac{2}{a^2 + 1} - \frac{4}{a^4 + 1} = \frac{8}{a^8 - 1}$

Prove: $\rm \frac{4x}{1 - x^2} + \frac{4x}{1 + x^2} + \frac{8x^3}{1 - x^4} = \frac{8x}{1-x^2}$

Prove: $\rm \frac{2xy}{x^2 - y^2} + \frac{2xy}{x^2 + y^2} + \frac{4x^3y}{x^4 + y^4} = \frac{8x^7y}{x^8 - y^8}$

Simplify: $\rm \frac{1}{a+b} + \frac{2a}{b^2 + a^2} + \frac{4a^3}{b^4 -a^4}$