Solve the following equation equation for \(x\) \[ x^2 + \frac{2x}{r^2} + \frac{1}{r^4} = 0 \]

If \( g(y) = \frac{y - 3}{11} + \frac{11}{y^2 - 9} \). what is \( g(y + 3) \)?

Simplify \( \frac{x-y}{x^{\frac{1}{3}}-x^{\frac{1}{3}}} \)

if a = -3, b = 2, c = 4, evaluate \( \frac{a^3-b^3-c^{\frac{1}{2}}}{b-a-c} \)

If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3

If (IPO3)4 = 11510 find P

What is the solution of the equation x2 - x - 1 + 0?

Factorize completely (x2 + x)2 - (2x + 2)2

If \( \frac{1}{p} = \frac{a^2+2ab+b^2}{a-b} \) and \( \frac{l}{q} = \frac{a+b}{a^2-2ab+b^2} \) Find \( \frac{p}{q} \)