Basic Math Examples

$\frac{(z + 4) (3 z - 11)}{z^{2}} \div (z + 4) \cdot \frac{8 z + 1}{z^{2}}$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{(z + 4) (3 z - 11)}{z^{2}}}{z + 4} \cdot \frac{8 z + 1}{z^{2}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{(z + 4) (3 z - 11)}{z^{2}} \cdot \frac{1}{z + 4} \cdot \frac{8 z + 1}{z^{2}}$

Step 3

Cancel the common factor of $z + 4$ .

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Step 3.1

Cancel the common factor.

$\frac{(z + 4) (3 z - 11)}{z^{2}} \cdot \frac{1}{z + 4} \cdot \frac{8 z + 1}{z^{2}}$

Step 3.2

Rewrite the expression.

$\frac{3 z - 11}{z^{2}} \cdot \frac{8 z + 1}{z^{2}}$

Step 4

Multiply $\frac{3 z - 11}{z^{2}} \cdot \frac{8 z + 1}{z^{2}}$ .

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Step 4.1

Multiply $\frac{3 z - 11}{z^{2}}$ by $\frac{8 z + 1}{z^{2}}$ .

$\frac{(3 z - 11) (8 z + 1)}{z^{2} z^{2}}$

Step 4.2

Multiply $z^{2}$ by $z^{2}$ by adding the exponents.

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Step 4.2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(3 z - 11) (8 z + 1)}{z^{2 + 2}}$

Step 4.2.2

Add $2$ and $2$ .

$\frac{(3 z - 11) (8 z + 1)}{z^{4}}$