Basic Math Examples

$\frac{z^{2} - 13}{49 z + 294} \div \frac{z - 6}{42}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{z^{2} - 13}{49 z + 294} \cdot \frac{42}{z - 6}$

Step 2

Factor $49$ out of $49 z + 294$ .

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Step 2.1

Factor $49$ out of $49 z$ .

$\frac{z^{2} - 13}{49 (z) + 294} \cdot \frac{42}{z - 6}$

Step 2.2

Factor $49$ out of $294$ .

$\frac{z^{2} - 13}{49 z + 49 \cdot 6} \cdot \frac{42}{z - 6}$

Step 2.3

Factor $49$ out of $49 z + 49 \cdot 6$ .

$\frac{z^{2} - 13}{49 (z + 6)} \cdot \frac{42}{z - 6}$

Step 3

Cancel the common factor of $7$ .

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Step 3.1

Factor $7$ out of $49 (z + 6)$ .

$\frac{z^{2} - 13}{7 (7 (z + 6))} \cdot \frac{42}{z - 6}$

Step 3.2

Factor $7$ out of $42$ .

$\frac{z^{2} - 13}{7 (7 (z + 6))} \cdot \frac{7 (6)}{z - 6}$

Step 3.3

Cancel the common factor.

$\frac{z^{2} - 13}{7 (7 (z + 6))} \cdot \frac{7 \cdot 6}{z - 6}$

Step 3.4

Rewrite the expression.

$\frac{z^{2} - 13}{7 (z + 6)} \cdot \frac{6}{z - 6}$

Step 4

Multiply $\frac{z^{2} - 13}{7 (z + 6)}$ by $\frac{6}{z - 6}$ .

$\frac{(z^{2} - 13) \cdot 6}{7 (z + 6) (z - 6)}$

Step 5

Move $6$ to the left of $z^{2} - 13$ .

$\frac{6 (z^{2} - 13)}{7 (z + 6) (z - 6)}$