8. Rational Expressions and Functions

Simplify each expression.

$\frac{x^2-10x+24}{(4-x)(6-x)}$

Determine the domain of the function $f\left(x\right)$.

$f\left(x\right)=\frac{5}{x}$

Determine the domain of the function $g\left(x\right)$.

$g\left(x\right)=\frac{x+1}{x^2-9}$

Given the function below, evaluate $f\left(0\right)$

$f\left(x\right)=\frac{3x+4}{x^2+7x+20}$

Determine the domain of the function $h\left(x\right)$.

$h\left(x\right)=\frac{x^2-2x-8}{x^2-5x+4}$

Determine the domain of the function $f\left(x\right)$.

$f\left(x\right)=\frac{7}{x-3}$

Simplify each expression.

$\frac{x-7}{7-x}$

Given the function below, evaluate $f\left(2\right)$

$f\left(x\right)=\frac{3}{11-x}$

Simplify the rational expressions below:

$\frac{6x}{12x}$

Simplify the rational expressions below:

$\frac{x^2+5x+6}{x^2+7x+10}$

Simplify the rational expressions below:

$\frac{x^2-4x}{x^2-2x-8x}$

Simplify the rational expressions below:

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

Simplify each expression.

$\frac{x^2-16}{16-x^2}$