Basic Math Examples

$\frac{5 c^{3} d^{4}}{40 c^{5} \cdot 2 + 5 c^{4} d^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Factor $5 c^{4}$ out of $40 c^{5} \cdot 2 + 5 c^{4} d^{2}$ .

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Step 1.1.1

Factor $5 c^{4}$ out of $40 c^{5} \cdot 2$ .

$\frac{5 c^{3} d^{4}}{5 c^{4} (8 c \cdot 2) + 5 c^{4} d^{2}}$

Step 1.1.2

Factor $5 c^{4}$ out of $5 c^{4} d^{2}$ .

$\frac{5 c^{3} d^{4}}{5 c^{4} (8 c \cdot 2) + 5 c^{4} (d^{2})}$

Step 1.1.3

Factor $5 c^{4}$ out of $5 c^{4} (8 c \cdot 2) + 5 c^{4} (d^{2})$ .

$\frac{5 c^{3} d^{4}}{5 c^{4} (8 c \cdot 2 + d^{2})}$

Step 1.2

Multiply $2$ by $8$ .

$\frac{5 c^{3} d^{4}}{5 c^{4} (16 c + d^{2})}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $5$ .

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Step 2.1.1

Cancel the common factor.

$\frac{5 c^{3} d^{4}}{5 c^{4} (16 c + d^{2})}$

Step 2.1.2

Rewrite the expression.

$\frac{c^{3} d^{4}}{c^{4} (16 c + d^{2})}$

Step 2.2

Cancel the common factor of $c^{3}$ and $c^{4}$ .

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Step 2.2.1

Factor $c^{3}$ out of $c^{3} d^{4}$ .

$\frac{c^{3} (d^{4})}{c^{4} (16 c + d^{2})}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $c^{3}$ out of $c^{4} (16 c + d^{2})$ .

$\frac{c^{3} (d^{4})}{c^{3} (c (16 c + d^{2}))}$

Step 2.2.2.2

Cancel the common factor.

$\frac{c^{3} d^{4}}{c^{3} (c (16 c + d^{2}))}$

Step 2.2.2.3

Rewrite the expression.

$\frac{d^{4}}{c (16 c + d^{2})}$