Basic Math Examples

$\frac{y^{2} + 17 y}{y^{2} - 6 y} + \frac{y^{2} - 4 y}{y^{2} - 6 y}$

Step 1

Combine the numerators over the common denominator.

$\frac{y^{2} + 17 y + y^{2} - 4 y}{y^{2} - 6 y}$

Step 2

Add $y^{2}$ and $y^{2}$ .

$\frac{2 y^{2} + 17 y - 4 y}{y^{2} - 6 y}$

Step 3

Subtract $4 y$ from $17 y$ .

$\frac{2 y^{2} + 13 y}{y^{2} - 6 y}$

Step 4

Factor $y$ out of $2 y^{2} + 13 y$ .

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Step 4.1

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

$\frac{y (2 y) + 13 y}{y^{2} - 6 y}$

Step 4.2

Factor $y$ out of $13 y$ .

$\frac{y (2 y) + y \cdot 13}{y^{2} - 6 y}$

Step 4.3

Factor $y$ out of $y (2 y) + y \cdot 13$ .

$\frac{y (2 y + 13)}{y^{2} - 6 y}$

Step 5

Factor $y$ out of $y^{2} - 6 y$ .

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Step 5.1

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

$\frac{y (2 y + 13)}{y \cdot y - 6 y}$

Step 5.2

Factor $y$ out of $- 6 y$ .

$\frac{y (2 y + 13)}{y \cdot y + y \cdot - 6}$

Step 5.3

Factor $y$ out of $y \cdot y + y \cdot - 6$ .

$\frac{y (2 y + 13)}{y (y - 6)}$

Step 6

Cancel the common factor of $y$ .

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Step 6.1

Cancel the common factor.

$\frac{y (2 y + 13)}{y (y - 6)}$

Step 6.2

Rewrite the expression.

$\frac{2 y + 13}{y - 6}$