Algebra Examples

$\frac{\frac{25}{4 x}}{\frac{10 x^{2}}{8 x^{4}}}$

Step 1

Cancel the common factor of $10$ and $8$ .

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Step 1.1

Factor $2$ out of $10 x^{2}$ .

$\frac{\frac{25}{4 x}}{\frac{2 (5 x^{2})}{8 x^{4}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $8 x^{4}$ .

$\frac{\frac{25}{4 x}}{\frac{2 (5 x^{2})}{2 (4 x^{4})}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{25}{4 x}}{\frac{2 (5 x^{2})}{2 (4 x^{4})}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{25}{4 x}}{\frac{5 x^{2}}{4 x^{4}}}$

Step 2

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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Step 2.1

Factor $x^{2}$ out of $5 x^{2}$ .

$\frac{\frac{25}{4 x}}{\frac{x^{2} \cdot 5}{4 x^{4}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{2}$ out of $4 x^{4}$ .

$\frac{\frac{25}{4 x}}{\frac{x^{2} \cdot 5}{x^{2} (4 x^{2})}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{25}{4 x}}{\frac{x^{2} \cdot 5}{x^{2} (4 x^{2})}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{25}{4 x}}{\frac{5}{4 x^{2}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{4 x} \cdot \frac{4 x^{2}}{5}$

Step 4

Combine.

$\frac{25 (4 x^{2})}{4 x \cdot 5}$

Step 5

Cancel the common factor of $25$ and $5$ .

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Step 5.1

Factor $5$ out of $25 (4 x^{2})$ .

$\frac{5 (5 (4 x^{2}))}{4 x \cdot 5}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $4 x \cdot 5$ .

$\frac{5 (5 (4 x^{2}))}{5 \cdot (4 x)}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (5 (4 x^{2}))}{5 \cdot (4 x)}$

Step 5.2.3

Rewrite the expression.

$\frac{5 (4 x^{2})}{4 x}$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Cancel the common factor.

$\frac{5 (4 x^{2})}{4 x}$

Step 6.2

Rewrite the expression.

$\frac{5 (x^{2})}{x}$

Step 7

Cancel the common factor of $x^{2}$ and $x$ .

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Step 7.1

Factor $x$ out of $5 (x^{2})$ .

$\frac{x (5 (x))}{x}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{x (5 (x))}{x^{1}}$

Step 7.2.2

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

$\frac{x (5 (x))}{x \cdot 1}$

Step 7.2.3

Cancel the common factor.

$\frac{x (5 (x))}{x \cdot 1}$

Step 7.2.4

Rewrite the expression.

$\frac{5 (x)}{1}$

Step 7.2.5

Divide $5 (x)$ by $1$ .

$5 (x)$

$5 x$