Precalculus Examples

$\frac{15 x^{2} - 60 x}{6 x^{2} - 24 x}$

Step 1

Factor $15 x$ out of $15 x^{2} - 60 x$ .

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Step 1.1

Factor $15 x$ out of $15 x^{2}$ .

$\frac{15 x (x) - 60 x}{6 x^{2} - 24 x}$

Step 1.2

Factor $15 x$ out of $- 60 x$ .

$\frac{15 x (x) + 15 x (- 4)}{6 x^{2} - 24 x}$

Step 1.3

Factor $15 x$ out of $15 x (x) + 15 x (- 4)$ .

$\frac{15 x (x - 4)}{6 x^{2} - 24 x}$

$\frac{15 x (x - 4)}{6 x^{2} - 24 x}$

Step 2

Factor $6 x$ out of $6 x^{2} - 24 x$ .

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Step 2.1

Factor $6 x$ out of $6 x^{2}$ .

$\frac{15 x (x - 4)}{6 x (x) - 24 x}$

Step 2.2

Factor $6 x$ out of $- 24 x$ .

$\frac{15 x (x - 4)}{6 x (x) + 6 x (- 4)}$

Step 2.3

Factor $6 x$ out of $6 x (x) + 6 x (- 4)$ .

$\frac{15 x (x - 4)}{6 x (x - 4)}$

$\frac{15 x (x - 4)}{6 x (x - 4)}$

Step 3

Cancel the common factor of $15$ and $6$ .

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Step 3.1

Factor $3$ out of $15 x (x - 4)$ .

$\frac{3 (5 x (x - 4))}{6 x (x - 4)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6 x (x - 4)$ .

$\frac{3 (5 x (x - 4))}{3 (2 x (x - 4))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (5 x (x - 4))}{3 (2 x (x - 4))}$

Step 3.2.3

Rewrite the expression.

$\frac{5 x (x - 4)}{2 x (x - 4)}$

$\frac{5 x (x - 4)}{2 x (x - 4)}$

$\frac{5 x (x - 4)}{2 x (x - 4)}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\frac{5 x (x - 4)}{2 x (x - 4)}$

Step 4.2

Rewrite the expression.

$\frac{5 (x - 4)}{2 (x - 4)}$

$\frac{5 (x - 4)}{2 (x - 4)}$

Step 5

Cancel the common factor of $x - 4$ .

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Step 5.1

Cancel the common factor.

$\frac{5 (x - 4)}{2 (x - 4)}$

Step 5.2

Rewrite the expression.

$\frac{5}{2}$

$\frac{5}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$

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