Pre-Algebra Examples

$\frac{4 p - 4}{p} \div \frac{9 p - 9}{4 p^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 p - 4}{p} \cdot \frac{4 p^{2}}{9 p - 9}$

Step 2

Cancel the common factor of $p$ .

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Step 2.1

Factor $p$ out of $4 p^{2}$ .

$\frac{4 p - 4}{p} \cdot \frac{p (4 p)}{9 p - 9}$

Step 2.2

Cancel the common factor.

$\frac{4 p - 4}{p} \cdot \frac{p (4 p)}{9 p - 9}$

Step 2.3

Rewrite the expression.

$(4 p - 4) \frac{4 p}{9 p - 9}$

$(4 p - 4) \frac{4 p}{9 p - 9}$

Step 3

Factor $9$ out of $9 p - 9$ .

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Step 3.1

Factor $9$ out of $9 p$ .

$(4 p - 4) \frac{4 p}{9 (p) - 9}$

Step 3.2

Factor $9$ out of $- 9$ .

$(4 p - 4) \frac{4 p}{9 (p) + 9 (- 1)}$

Step 3.3

Factor $9$ out of $9 (p) + 9 (- 1)$ .

$(4 p - 4) \frac{4 p}{9 (p - 1)}$

$(4 p - 4) \frac{4 p}{9 (p - 1)}$

Step 4

Multiply $4 p - 4$ by $\frac{4 p}{9 (p - 1)}$ .

$\frac{(4 p - 4) (4 p)}{9 (p - 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $4$ out of $4 p - 4$ .

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Step 5.1.1

Factor $4$ out of $4 p$ .

$\frac{(4 (p) - 4) \cdot 4 p}{9 (p - 1)}$

Step 5.1.2

Factor $4$ out of $- 4$ .

$\frac{(4 (p) + 4 (- 1)) \cdot 4 p}{9 (p - 1)}$

Step 5.1.3

Factor $4$ out of $4 (p) + 4 (- 1)$ .

$\frac{4 (p - 1) \cdot 4 p}{9 (p - 1)}$

$\frac{4 (p - 1) \cdot 4 p}{9 (p - 1)}$

Step 5.2

Multiply $4$ by $4$ .

$\frac{16 (p - 1) p}{9 (p - 1)}$

$\frac{16 (p - 1) p}{9 (p - 1)}$

Step 6

Cancel the common factor of $p - 1$ .

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Step 6.1

Cancel the common factor.

$\frac{16 (p - 1) p}{9 (p - 1)}$

Step 6.2

Rewrite the expression.

$\frac{16 p}{9}$

$\frac{16 p}{9}$

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