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Precalculus Examples

\frac{x^{2} (x - 1) (x + 5)}{x (x - 1)}

$\frac{x^{2} (x - 1) (x + 5)}{x (x - 1)}$

Step 1

Cancel the common factor of

x^{2}

$x^{2}$ and

x

$x$ .

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Step 1.1

Factor

x

$x$ out of

x^{2} (x - 1) (x + 5)

$x^{2} (x - 1) (x + 5)$ .

\frac{x ((x (x - 1)) (x + 5))}{x (x - 1)}

$\frac{x ((x (x - 1)) (x + 5))}{x (x - 1)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Cancel the common factor.

$\frac{x ((x (x - 1)) (x + 5))}{x (x - 1)}$

Step 1.2.2

Rewrite the expression.

$\frac{(x (x - 1)) (x + 5)}{x - 1}$

$\frac{(x (x - 1)) (x + 5)}{x - 1}$

$\frac{(x (x - 1)) (x + 5)}{x - 1}$

Step 2

Cancel the common factor of

$x - 1$ .

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Step 2.1

Cancel the common factor.

$\frac{x (x - 1) (x + 5)}{x - 1}$

Step 2.2

Divide

$(x) (x + 5)$ by

$1$ .

$(x) (x + 5)$

$(x) (x + 5)$

Step 3

Apply the distributive property.

$x \cdot x + x \cdot 5$

Step 4

Simplify the expression.

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Step 4.1

Multiply

$x$ by

$x$ .

$x^{2} + x \cdot 5$

Step 4.2

Move

$5$ to the left of

$x$ .

$x^{2} + 5 x$

$x^{2} + 5 x$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$