Domain & Simplifying Rational Expressions

Find the domain of
 $f\left(x\right)\ =\ \frac{4}{x-5}$ .

•  $ℝ-\left\{4\right\}$  

•  $ℝ-\left\{5\right\}$  

•  $ℝ-\left\{-4\right\}$  

•  $ℝ-\left\{-5\right\}$  

Find the domain of
 $f\left(x\right)=\frac{3x-2}{x^2-2x-3}$  .

•  $ℝ$  

•  $ℝ-\left\{-\frac{2}{3}\right\}$  

•  $ℝ-\left\{-3,1\right\}$  

•  $ℝ-\left\{-1,3\right\}$  

Find the domain of
 $f\left(x\right)\ =\ \frac{5x}{3x^2+12x-63}$ .

•  $ℝ-\left\{0\right\}$  

•  $ℝ-\left\{3\right\}$  

•  $ℝ-\left\{-7,3\right\}$  

•  $ℝ-\left\{\frac{2}{3},1\right\}$  

Find the domain of
 $f\left(x\right)\ =\ \frac{x^2+89x-192}{x^2+2x+1}$ . 

•  $ℝ$  

•  $ℝ-\left\{1\right\}$  

•  $ℝ-\left\{-1\right\}$  

•  $ℝ-\left\{-1,1\right\}$  

Simplify:  $\frac{2x-4}{x-2}$  

• Already simplified

•  $4$  

•  $2x+1$  

•  $2$  

Simplify:  $\frac{x-5}{x^2-10x+25}$  

•  $\frac{1}{x}-10x-\frac{1}{5}$  

•  $\frac{1}{x-5}$  

•  $x-5$  

•  $5$  

Simplify:  $\frac{6x^3+42x^2}{2x^2+26x+84}$  

• Already simplified

•  $\frac{6x^2}{x-6}$  

•  $\frac{x^2}{6\left(x+6\right)}$  

•  $\frac{3x^2}{x+6}$  

Simplify:  $\frac{x^2-6x+9}{x-3}\cdot\frac{x^2+3x-18}{\left(x-3\right)^2}$  

•  $1$  

•  $x-3$  

•  $x+6$  

•  $x-6$