Basic Math Examples

$\frac{- 9 c^{5}}{c} + \frac{5 c^{4}}{c}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{- 9 c^{5} + 5 c^{4}}{c}$

Step 1.2

Factor $c^{4}$ out of $- 9 c^{5} + 5 c^{4}$ .

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Step 1.2.1

Factor $c^{4}$ out of $- 9 c^{5}$ .

$\frac{c^{4} (- 9 c) + 5 c^{4}}{c}$

Step 1.2.2

Factor $c^{4}$ out of $5 c^{4}$ .

$\frac{c^{4} (- 9 c) + c^{4} \cdot 5}{c}$

Step 1.2.3

Factor $c^{4}$ out of $c^{4} (- 9 c) + c^{4} \cdot 5$ .

$\frac{c^{4} (- 9 c + 5)}{c}$

Step 1.3

Cancel the common factor of $c^{4}$ and $c$ .

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Step 1.3.1

Factor $c$ out of $c^{4} (- 9 c + 5)$ .

$\frac{c (c^{3} (- 9 c + 5))}{c}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Raise $c$ to the power of $1$ .

$\frac{c (c^{3} (- 9 c + 5))}{c^{1}}$

Step 1.3.2.2

Factor $c$ out of $c^{1}$ .

$\frac{c (c^{3} (- 9 c + 5))}{c \cdot 1}$

Step 1.3.2.3

Cancel the common factor.

$\frac{c (c^{3} (- 9 c + 5))}{c \cdot 1}$

Step 1.3.2.4

Rewrite the expression.

$\frac{c^{3} (- 9 c + 5)}{1}$

Step 1.3.2.5

Divide $c^{3} (- 9 c + 5)$ by $1$ .

$c^{3} (- 9 c + 5)$

Step 1.4

Apply the distributive property.

$c^{3} (- 9 c) + c^{3} \cdot 5$

Step 1.5

Reorder.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$- 9 c^{3} c + c^{3} \cdot 5$

Step 1.5.2

Move $5$ to the left of $c^{3}$ .

$- 9 c^{3} c + 5 \cdot c^{3}$

Step 2

Multiply $c^{3}$ by $c$ by adding the exponents.

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Step 2.1

Move $c$ .

$- 9 (c \cdot c^{3}) + 5 \cdot c^{3}$

Step 2.2

Multiply $c$ by $c^{3}$ .

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Step 2.2.1

Raise $c$ to the power of $1$ .

$- 9 (c^{1} c^{3}) + 5 \cdot c^{3}$

Step 2.2.2

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

$- 9 c^{1 + 3} + 5 \cdot c^{3}$

Step 2.3

Add $1$ and $3$ .

$- 9 c^{4} + 5 \cdot c^{3}$

$- 9 c^{4} + 5 c^{3}$