Algebra Examples

$\frac{(25 x^{4}) \frac{1}{2}}{15 x^{2}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $25$ and $15$ .

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Step 1.1.1

Factor $5$ out of $(25 x^{4}) (\frac{1}{2})$ .

$\frac{5 (5 x^{4} \frac{1}{2})}{15 x^{2}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $5$ out of $15 x^{2}$ .

$\frac{5 (5 x^{4} \frac{1}{2})}{5 (3 x^{2})}$

Step 1.1.2.2

Cancel the common factor.

$\frac{5 (5 x^{4} \frac{1}{2})}{5 (3 x^{2})}$

Step 1.1.2.3

Rewrite the expression.

$\frac{5 x^{4} \frac{1}{2}}{3 x^{2}}$

Step 1.2

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

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Step 1.2.1

Factor $x^{2}$ out of $5 x^{4} \frac{1}{2}$ .

$\frac{x^{2} (5 x^{2} \frac{1}{2})}{3 x^{2}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x^{2}$ out of $3 x^{2}$ .

$\frac{x^{2} (5 x^{2} \frac{1}{2})}{x^{2} \cdot 3}$

Step 1.2.2.2

Cancel the common factor.

$\frac{x^{2} (5 x^{2} \frac{1}{2})}{x^{2} \cdot 3}$

Step 1.2.2.3

Rewrite the expression.

$\frac{5 x^{2} \frac{1}{2}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

Combine $5$ and $\frac{1}{2}$ .

$\frac{x^{2} \frac{5}{2}}{3}$

Step 2.2

Combine $x^{2}$ and $\frac{5}{2}$ .

$\frac{\frac{x^{2} \cdot 5}{2}}{3}$

Step 3

Move $5$ to the left of $x^{2}$ .

$\frac{\frac{5 x^{2}}{2}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 x^{2}}{2} \cdot \frac{1}{3}$

Step 5

Combine.

$\frac{5 x^{2} \cdot 1}{2 \cdot 3}$

Step 6

Multiply.

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Step 6.1

Multiply $5$ by $1$ .

$\frac{5 x^{2}}{2 \cdot 3}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{5 x^{2}}{6}$