Finite Math Examples

$\frac{y^{2} + 5 y}{y^{2} + 10 y + 25}$

Step 1

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

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Step 1.1

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

$\frac{y \cdot y + 5 y}{y^{2} + 10 y + 25}$

Step 1.2

Factor $y$ out of $5 y$ .

$\frac{y \cdot y + y \cdot 5}{y^{2} + 10 y + 25}$

Step 1.3

Factor $y$ out of $y \cdot y + y \cdot 5$ .

$\frac{y (y + 5)}{y^{2} + 10 y + 25}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

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

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 y = 2 \cdot y \cdot 5$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 5$ .

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

Step 3

Cancel the common factor of $y + 5$ and ${(y + 5)}^{2}$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{(y + 5) y}{(y + 5) (y + 5)}$

Step 3.2.2

Cancel the common factor.

$\frac{(y + 5) y}{(y + 5) (y + 5)}$

Step 3.2.3

Rewrite the expression.

$\frac{y}{y + 5}$