# How do you find the restricted values of x or the rational expression (x^2+x+15)/(x^2-3x)?

Feb 27, 2016

Restrictions on $x$ are given by $x \ne 0$ and $x \ne 3$.

#### Explanation:

The rational expression (x^2+x+15)/(x^2−3x), cannot be defined if denominator i.e. ${x}^{2} - 3 x = 0$ i.e. $x \left(x - 3\right) = 0$

i.e. $x$ cannot take values $\left\{0 , 3\right\}$.

Hence, restrictions on $x$ are given by $x \ne 0$ and $x \ne 3$

The values of $x$ that the rational expression has a meaning are all the reals that dont nullify the denominator hence

${x}^{2} - 3 x = 0 \implies x \left(x - 3\right) = 0 \implies x = 0 \mathmr{and} x = 3$

Hence the domain is $R - \left\{0 , 3\right\}$ where $R$ is the set of reals.