Determine the domain of a rational function Precalculus

Determine the domain of the functions given by the following expressions.

f\left(x\right)=\dfrac{2x^2+3x}{3x^2-2}

\mathbb{R}

\mathbb{R}- \left\{ \dfrac{2}{3} \right\}

\mathbb{R} - \left\{ \sqrt{\dfrac{2}{3}} \right\}

\mathbb{R} - \left\{ \sqrt{\dfrac{2}{3}},-\sqrt{\dfrac{2}{3}} \right\}

f\left(x\right)=\dfrac{4x+1}{x^2+2}

\mathbb{R}

\mathbb{R} - \left\{ \sqrt{2} \right\}

\mathbb{R} -\left\{ -\sqrt{{2}} \right\}

\mathbb{R} - \left\{ -\sqrt{{2}},\sqrt{{2}} \right\}

f\left(x\right)=\dfrac{2-x^2}{4x+x^3}

\mathbb{R}

\mathbb{R}- \left\{0 \right\}

\mathbb{R} - \{-2{,}2}\

\mathbb{R}-\{-2, 0, 2}\

f\left(x\right)=\dfrac{x^3-7x^2+1}{4x^2-25}

\mathbb{R}

\mathbb{R}-\left\{ -\dfrac{25}{4}, \dfrac{25}{4} \right\}

\mathbb{R} - \left\{ {-\dfrac{5}{2}},{\dfrac{5}{2}} \right\}

\mathbb{R} - \left\{ -{\dfrac{2}{5}},{\dfrac{2}{5}} \right\}

f\left(x\right)=\dfrac{x^2-1}{x^2-5x+6}

\mathbb{R}

\mathbb{R} - \{ 1{,}5}\

\mathbb{R} - \{ -2,-3}\

\mathbb{R} - \{ 2{,}3}\

f\left(x\right)=\dfrac{x}{x^2-2x+1}

\mathbb{R}

\mathbb{R} - \{-1{,}1\}

\mathbb{R}- \{1\}

\mathbb{R} - \{-1\}

f\left(x\right)=\dfrac{2x-1}{x^2+x^3}

\mathbb{R}

\mathbb{R} - \{-1{,}0\}

\mathbb{R} -\{0{,}1\}

\mathbb{R} - \{0\}