Perform the indicated operation and simplify the result. Leave your answer in factored form. \[ \frac{x}{x+6}+\frac{5 x-1}{x-6} \] \( \frac{x}{x+6}+\frac{5 x-1}{x-6}=\square \)

Divide. If there is a remainder, include it as a simplified fraction. \[ \left(14 m^{2}+8\right) \div 2 m^{2} \]

Evaluate \( \frac{1}{4} x^{4}-\frac{1}{2} x^{2} \) for \( x=2 \) \( -1 \frac{15}{16} \) 3 2 \( -\frac{15}{16} \)

11. Una función cuadrática \( f \) y una función \( g \) lineal. Satisfacen las siguientes condiciones: \( g(0)=2 \), \( f(0)=3, f(x+1)-f(x)=2 x+5 \). Si \( (f+g)(-1)=6 \) determine la regla de correspondencia de \( (f . g) \)

2.2 Solve \( x \) and \( y: \) \( y-2 x=-1 \quad \) and \( \quad y^{2}-3 x y=-2 \) If \( \frac{x}{y}+\frac{y}{x}=\frac{17}{4} \), calculate two values of \( \frac{x}{y} \)

Solve the inequality for \( y \). \[ 4(3 y+9)<7 y+11 \] Simplify your answer as much as possible.