Subtract (8z^4)/(8z+20)-2/(z^5)

$\frac{8 z^{4}}{8 z + 20} - \frac{2}{z^{5}}$

Cancel the common factor of $8$ and $8 z + 20$ .

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Factor $4$ out of $8 z^{4}$ .

$\frac{4 (2 z^{4})}{8 z + 20} - \frac{2}{z^{5}}$

Cancel the common factors.

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Factor $4$ out of $8 z$ .

$\frac{4 (2 z^{4})}{4 (2 z) + 20} - \frac{2}{z^{5}}$

Factor $4$ out of $20$ .

$\frac{4 (2 z^{4})}{4 (2 z) + 4 (5)} - \frac{2}{z^{5}}$

Factor $4$ out of $4 (2 z) + 4 (5)$ .

$\frac{4 (2 z^{4})}{4 (2 z + 5)} - \frac{2}{z^{5}}$

Cancel the common factor.

$\frac{4 (2 z^{4})}{4 (2 z + 5)} - \frac{2}{z^{5}}$

Rewrite the expression.

$\frac{2 z^{4}}{2 z + 5} - \frac{2}{z^{5}}$

To write $\frac{2 z^{4}}{2 z + 5}$ as a fraction with a common denominator, multiply by $\frac{z^{5}}{z^{5}}$ .

$\frac{2 z^{4}}{2 z + 5} \cdot \frac{z^{5}}{z^{5}} - \frac{2}{z^{5}}$

To write $- \frac{2}{z^{5}}$ as a fraction with a common denominator, multiply by $\frac{2 z + 5}{2 z + 5}$ .

$\frac{2 z^{4}}{2 z + 5} \cdot \frac{z^{5}}{z^{5}} - \frac{2}{z^{5}} \cdot \frac{2 z + 5}{2 z + 5}$

Write each expression with a common denominator of $(2 z + 5) z^{5}$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{2 z^{4}}{2 z + 5}$ and $\frac{z^{5}}{z^{5}}$ .

$\frac{2 z^{4} z^{5}}{(2 z + 5) z^{5}} - \frac{2}{z^{5}} \cdot \frac{2 z + 5}{2 z + 5}$

Multiply $\frac{2}{z^{5}}$ and $\frac{2 z + 5}{2 z + 5}$ .

$\frac{2 z^{4} z^{5}}{(2 z + 5) z^{5}} - \frac{2 (2 z + 5)}{z^{5} (2 z + 5)}$

Reorder the factors of $(2 z + 5) z^{5}$ .

$\frac{2 z^{4} z^{5}}{z^{5} (2 z + 5)} - \frac{2 (2 z + 5)}{z^{5} (2 z + 5)}$

Combine the numerators over the common denominator.

$\frac{2 z^{4} z^{5} - 2 (2 z + 5)}{z^{5} (2 z + 5)}$

Simplify the numerator.

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Factor $2$ out of $2 z^{4} z^{5} - 2 (2 z + 5)$ .

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Factor $2$ out of $2 z^{4} z^{5}$ .

$\frac{2 (z^{4} z^{5}) - 2 (2 z + 5)}{z^{5} (2 z + 5)}$

Factor $2$ out of $- 2 (2 z + 5)$ .

$\frac{2 (z^{4} z^{5}) + 2 (- (2 z + 5))}{z^{5} (2 z + 5)}$

Factor $2$ out of $2 (z^{4} z^{5}) + 2 (- (2 z + 5))$ .

$\frac{2 (z^{4} z^{5} - (2 z + 5))}{z^{5} (2 z + 5)}$

Multiply $z^{4}$ by $z^{5}$ by adding the exponents.

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

$\frac{2 (z^{4 + 5} - (2 z + 5))}{z^{5} (2 z + 5)}$

Add $4$ and $5$ .

$\frac{2 (z^{9} - (2 z + 5))}{z^{5} (2 z + 5)}$

Apply the distributive property.

$\frac{2 (z^{9} - (2 z) - 1 \cdot 5)}{z^{5} (2 z + 5)}$

Multiply $2$ by $- 1$ .

$\frac{2 (z^{9} - 2 z - 1 \cdot 5)}{z^{5} (2 z + 5)}$

Multiply $- 1$ by $5$ .

$\frac{2 (z^{9} - 2 z - 5)}{z^{5} (2 z + 5)}$

Subtract (8z^4)/(8z+20)-2/(z^5)

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