Pre-Algebra Examples

$\frac{c^{2 + 3 c}}{c^{2 + 2 c - 3}} \div \frac{c}{c + 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{c^{2 + 3 c}}{c^{2 + 2 c - 3}} \cdot \frac{c + 1}{c}$

Step 2

Cancel the common factor of $c^{2 + 3 c}$ and $c^{2 + 2 c - 3}$ .

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Step 2.1

Factor $c^{2 + 2 c - 3}$ out of $c^{2 + 3 c}$ .

$\frac{c^{2 + 2 c - 3} c^{2 + 3 c - (2 + 2 c - 3)}}{c^{2 + 2 c - 3}} \cdot \frac{c + 1}{c}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{c^{2 + 2 c - 3} c^{2 + 3 c - (2 + 2 c - 3)}}{c^{2 + 2 c - 3} \cdot 1} \cdot \frac{c + 1}{c}$

Step 2.2.2

Cancel the common factor.

$\frac{c^{2 + 2 c - 3} c^{2 + 3 c - (2 + 2 c - 3)}}{c^{2 + 2 c - 3} \cdot 1} \cdot \frac{c + 1}{c}$

Step 2.2.3

Rewrite the expression.

$\frac{c^{2 + 3 c - (2 + 2 c - 3)}}{1} \cdot \frac{c + 1}{c}$

Step 2.2.4

Divide $c^{2 + 3 c - (2 + 2 c - 3)}$ by $1$ .

$c^{2 + 3 c - (2 + 2 c - 3)} \frac{c + 1}{c}$

Step 3

Simplify each term.

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Step 3.1

Subtract $3$ from $2$ .

$c^{2 + 3 c - (2 c - 1)} \frac{c + 1}{c}$

Step 3.2

Apply the distributive property.

$c^{2 + 3 c - (2 c) - - 1} \frac{c + 1}{c}$

Step 3.3

Multiply $2$ by $- 1$ .

$c^{2 + 3 c - 2 c - - 1} \frac{c + 1}{c}$

Step 3.4

Multiply $- 1$ by $- 1$ .

$c^{2 + 3 c - 2 c + 1} \frac{c + 1}{c}$

Step 4

Add $2$ and $1$ .

$c^{3 c - 2 c + 3} \frac{c + 1}{c}$

Step 5

Subtract $2 c$ from $3 c$ .

$c^{c + 3} \frac{c + 1}{c}$

Step 6

Combine $c^{c + 3}$ and $\frac{c + 1}{c}$ .

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

Step 7

Cancel the common factor of $c^{c + 3}$ and $c$ .

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Step 7.1

Factor $c$ out of $c^{c + 3} (c + 1)$ .

$\frac{c (c^{c + 2} (c + 1))}{c}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{c (c^{c + 2} (c + 1))}{c^{1}}$

Step 7.2.2

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

$\frac{c (c^{c + 2} (c + 1))}{c \cdot 1}$

Step 7.2.3

Cancel the common factor.

$\frac{c (c^{c + 2} (c + 1))}{c \cdot 1}$

Step 7.2.4

Rewrite the expression.

$\frac{c^{c + 2} (c + 1)}{1}$

Step 7.2.5

Divide $c^{c + 2} (c + 1)$ by $1$ .

$c^{c + 2} (c + 1)$

Step 8

Apply the distributive property.

$c^{c + 2} c + c^{c + 2} \cdot 1$

Step 9

Multiply $c^{c + 2}$ by $c$ by adding the exponents.

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Step 9.1

Multiply $c^{c + 2}$ by $c$ .

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Step 9.1.1

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

$c^{c + 2} c^{1} + c^{c + 2} \cdot 1$

Step 9.1.2

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

$c^{c + 2 + 1} + c^{c + 2} \cdot 1$

Step 9.2

Add $2$ and $1$ .

$c^{c + 3} + c^{c + 2} \cdot 1$

Step 10

Multiply $c^{c + 2}$ by $1$ .

$c^{c + 3} + c^{c + 2}$