Algebra Examples

$\frac{6 x^{2}}{5 y} \div \frac{3 x}{10 y^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 x^{2}}{5 y} \cdot \frac{10 y^{2}}{3 x}$

Step 2

Combine.

$\frac{6 x^{2} (10 y^{2})}{5 y (3 x)}$

Step 3

Cancel the common factor of $6$ and $3$ .

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Step 3.1

Factor $3$ out of $6 x^{2} (10 y^{2})$ .

$\frac{3 (2 x^{2} (10 y^{2}))}{5 y (3 x)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $5 y (3 x)$ .

$\frac{3 (2 x^{2} (10 y^{2}))}{3 (5 y (x))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (2 x^{2} (10 y^{2}))}{3 (5 y (x))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 x^{2} (10 y^{2})}{5 y (x)}$

$\frac{2 x^{2} (10 y^{2})}{5 y (x)}$

$\frac{2 x^{2} (10 y^{2})}{5 y (x)}$

Step 4

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

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Step 4.1

Factor $x$ out of $2 x^{2} (10 y^{2})$ .

$\frac{x (2 x (10 y^{2}))}{5 y (x)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $5 y (x)$ .

$\frac{x (2 x (10 y^{2}))}{x (5 y)}$

Step 4.2.2

Cancel the common factor.

$\frac{x (2 x (10 y^{2}))}{x (5 y)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 x (10 y^{2})}{5 y}$

$\frac{2 x (10 y^{2})}{5 y}$

$\frac{2 x (10 y^{2})}{5 y}$

Step 5

Cancel the common factor of $10$ and $5$ .

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Step 5.1

Factor $5$ out of $2 x (10 y^{2})$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $5 y$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

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

$\frac{y (2 x (2 y))}{y}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{y (2 x (2 y))}{y^{1}}$

Step 6.2.2

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

$\frac{y (2 x (2 y))}{y \cdot 1}$

Step 6.2.3

Cancel the common factor.

$\frac{y (2 x (2 y))}{y \cdot 1}$

Step 6.2.4

Rewrite the expression.

$\frac{2 x (2 y)}{1}$

Step 6.2.5

Divide $2 x (2 y)$ by $1$ .

$2 x (2 y)$

$2 x (2 y)$

$2 x (2 y)$

Step 7

Simplify the expression.

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Step 7.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x y$

Step 7.2

Multiply $2$ by $2$ .

$4 x y$

$4 x y$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$