Fractions

Algebra: Adding and subtracting fractions

Fractions

Fractions with variables

Variables can occur in both the $\orange{\text{numerator}}$ as well as the $\blue{\text{denominator }}$ of fraction. Just like a fraction with numbers, the $\blue{\text{denominator }}$ cannot be equal to $0$ . Therefore, we cannot enter numbers for which the denominator is equal to $0$ . Most of the time, we will not mention this explicitly, but will assume this value is not entered.

Examples

$\frac{\orange{x+3}}{\blue{x-5}}$

$\frac{\orange{x}}{\blue{x^2-1}}$

Denominator not equal to 0

Since the $\blue{\text{denominator }}$ can not be equal to $0$ , the following assumptions hold for the variables.

$\begin{array}{rcl} \dfrac{\orange{x+3}}{\blue{x-5}}&&x \ne 5 \\ \\ \dfrac{\orange{x}}{\blue{x^2-1}} && x \ne 1 \text{ and } x \ne -1\end{array}$

Calculate the following fraction for $x=4$ :

${{\left(x-1\right)\cdot \left(x^2+x\right)}\over{x}}$
Simplify the answer to a simplified fraction or integer.

$15$

This result can be found by replacing $x$ with $4$ everywhere:
$\displaystyle {{\left(4-1\right)\cdot \left(4^2+4\right)}\over{4}}= 15\tiny.$

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