Questions

Simplify: $\rm \frac{a^2 + b^2}{ab} - \frac{b^2}{a(a+b)} - \frac{a^2}{b(a+b)}$

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

Simplify: $\rm \frac{x^2}{y(x+y)} + \frac{y^2}{x(x+y)}$

Simplify: $\rm \frac{x^2}{y(x-y)} + \frac{y^2}{x(y-x)}$

Prove that the values of x in the equation 5.4^x+1 + 16^x = 64 also satisfy the equation 9^x = 4.3^x+1 - 27.

Prove that the values of x in the equation 3^x-3 + 3^4-x = 4 also satisfy the equation 4^x-4 + 4^3-x = 1 (¼).

Prove that the values of x in the equation 3^x-2 + 3^3-x = 4 also satisfy the equation 4^x - 6.2^x+1 + 32 = 0.

Solve: 2^4x+5.a^1-x = 4^x+32a^x-1

Solve: 2^x-3 .2a^1-x = 2^3x-5.a^x-2

Solve: 3^x + 3^x+1 + 3^x+2 + 3^x+4 = 846