Basic Math Examples

$\frac{z - 7}{2 z - 12} \cdot \frac{5 z - 30}{z^{2} - 49}$

Step 1

Simplify with factoring out.

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Step 1.1

Factor $2$ out of $2 z - 12$ .

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Step 1.1.1

Factor $2$ out of $2 z$ .

$\frac{z - 7}{2 (z) - 12} \cdot \frac{5 z - 30}{z^{2} - 49}$

Step 1.1.2

Factor $2$ out of $- 12$ .

$\frac{z - 7}{2 z + 2 \cdot - 6} \cdot \frac{5 z - 30}{z^{2} - 49}$

Step 1.1.3

Factor $2$ out of $2 z + 2 \cdot - 6$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 z - 30}{z^{2} - 49}$

Step 1.2

Factor $5$ out of $5 z - 30$ .

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Step 1.2.1

Factor $5$ out of $5 z$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 (z) - 30}{z^{2} - 49}$

Step 1.2.2

Factor $5$ out of $- 30$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 z + 5 \cdot - 6}{z^{2} - 49}$

Step 1.2.3

Factor $5$ out of $5 z + 5 \cdot - 6$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 (z - 6)}{z^{2} - 49}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 (z - 6)}{z^{2} - 7^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = z$ and $b = 7$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 (z - 6)}{(z + 7) (z - 7)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $z - 7$ .

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Step 3.1.1

Factor $z - 7$ out of $(z + 7) (z - 7)$ .

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 (z - 6)}{(z - 7) (z + 7)}$

Step 3.1.2

Cancel the common factor.

$\frac{z - 7}{2 (z - 6)} \cdot \frac{5 (z - 6)}{(z - 7) (z + 7)}$

Step 3.1.3

Rewrite the expression.

$\frac{1}{2 (z - 6)} \cdot \frac{5 (z - 6)}{z + 7}$

Step 3.2

Cancel the common factor of $z - 6$ .

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Step 3.2.1

Factor $z - 6$ out of $2 (z - 6)$ .

$\frac{1}{(z - 6) \cdot 2} \cdot \frac{5 (z - 6)}{z + 7}$

Step 3.2.2

Factor $z - 6$ out of $5 (z - 6)$ .

$\frac{1}{(z - 6) \cdot 2} \cdot \frac{(z - 6) \cdot 5}{z + 7}$

Step 3.2.3

Cancel the common factor.

$\frac{1}{(z - 6) \cdot 2} \cdot \frac{(z - 6) \cdot 5}{z + 7}$

Step 3.2.4

Rewrite the expression.

$\frac{1}{2} \cdot \frac{5}{z + 7}$

Step 3.3

Multiply $\frac{1}{2}$ by $\frac{5}{z + 7}$ .

$\frac{5}{2 (z + 7)}$