Algebra Examples

$\frac{\frac{4 c^{2} - 1}{3 c}}{\frac{2 c + 1}{9 c^{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 c^{2} - 1}{3 c} \cdot \frac{9 c^{2}}{2 c + 1}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3 c$ .

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Step 2.1.1

Factor $3 c$ out of $9 c^{2}$ .

$\frac{4 c^{2} - 1}{3 c} \cdot \frac{3 c (3 c)}{2 c + 1}$

Step 2.1.2

Cancel the common factor.

$\frac{4 c^{2} - 1}{3 c} \cdot \frac{3 c (3 c)}{2 c + 1}$

Step 2.1.3

Rewrite the expression.

$(4 c^{2} - 1) \frac{3 c}{2 c + 1}$

Step 2.2

Multiply $4 c^{2} - 1$ by $\frac{3 c}{2 c + 1}$ .

$\frac{(4 c^{2} - 1) (3 c)}{2 c + 1}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $4 c^{2}$ as ${(2 c)}^{2}$ .

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

Step 3.2

Rewrite $1$ as $1^{2}$ .

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

Step 3.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 c$ and $b = 1$ .

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $2 c + 1$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Divide $(2 c - 1) \cdot 3 c$ by $1$ .

$(2 c - 1) \cdot 3 c$

Step 4.2

Apply the distributive property.

$(2 c \cdot 3 - 1 \cdot 3) c$

Step 4.3

Multiply.

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Step 4.3.1

Multiply $3$ by $2$ .

$(6 c - 1 \cdot 3) c$

Step 4.3.2

Multiply $- 1$ by $3$ .

$(6 c - 3) c$

Step 4.4

Apply the distributive property.

$6 c \cdot c - 3 c$

Step 5

Multiply $c$ by $c$ by adding the exponents.

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Step 5.1

Move $c$ .

$6 (c \cdot c) - 3 c$

Step 5.2

Multiply $c$ by $c$ .

$6 c^{2} - 3 c$