Operations with Rational Expressions

Simplify the rational expression $$\frac{6x}{24x^2-216x}$$

Simplify the rational expression $$\frac{x^2-6x-16}{x^2-5x-14}$$

Identify the LCM of: $$x^2-49\ and\ x+7$$

Keep your answer in factored form.

Identify the LCM of: $$x-7\ and\ x+4$$

Keep your answer in factored form.

Simplify using the given operation

$$\frac{6x+4}{2x-3}+\frac{3x-9}{2x-3}$$

Simplify using the given operation

$$\frac{12}{x^2-9}+\frac{2}{x+3}$$

Simplify using the given operation

$$\frac{7}{6x}-\frac{3}{8x}$$

Simplify using the given operation

$$\frac{6}{x+4}+\frac{2}{x-6}$$

Simplify using the given operation

$$\frac{x+10}{9-x}\cdot\frac{x^2-5x-36}{4x^2+16x}$$

Simplify using the given operation

$$\frac{2x+2}{x+2}\div\frac{4x^2+8x+4}{12x+12}$$