Algebra Examples

$\frac{5 y^{2} + 10 y}{6 y^{4} + 12 y^{3}}$

Step 1

Factor $5 y$ out of $5 y^{2} + 10 y$ .

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Step 1.1

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

$\frac{5 y (y) + 10 y}{6 y^{4} + 12 y^{3}}$

Step 1.2

Factor $5 y$ out of $10 y$ .

$\frac{5 y (y) + 5 y (2)}{6 y^{4} + 12 y^{3}}$

Step 1.3

Factor $5 y$ out of $5 y (y) + 5 y (2)$ .

$\frac{5 y (y + 2)}{6 y^{4} + 12 y^{3}}$

$\frac{5 y (y + 2)}{6 y^{4} + 12 y^{3}}$

Step 2

Factor $6 y^{3}$ out of $6 y^{4} + 12 y^{3}$ .

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Step 2.1

Factor $6 y^{3}$ out of $6 y^{4}$ .

$\frac{5 y (y + 2)}{6 y^{3} (y) + 12 y^{3}}$

Step 2.2

Factor $6 y^{3}$ out of $12 y^{3}$ .

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

Step 2.3

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

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

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

Step 3

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

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Step 3.1

Factor $y$ out of $5 y (y + 2)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{y (5 (y + 2))}{y (6 y^{2} (y + 2))}$

Step 3.2.2

Cancel the common factor.

$\frac{y (5 (y + 2))}{y (6 y^{2} (y + 2))}$

Step 3.2.3

Rewrite the expression.

$\frac{5 (y + 2)}{6 y^{2} (y + 2)}$

$\frac{5 (y + 2)}{6 y^{2} (y + 2)}$

$\frac{5 (y + 2)}{6 y^{2} (y + 2)}$

Step 4

Cancel the common factor of $y + 2$ .

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Step 4.1

Cancel the common factor.

$\frac{5 (y + 2)}{6 y^{2} (y + 2)}$

Step 4.2

Rewrite the expression.

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

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

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