Algebra Examples

$\frac{2 y}{y^{2} - 5 y} - \frac{- 3 y}{y - 5}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

$\frac{2 y}{y \cdot y - 5 y} - \frac{- 3 y}{y - 5}$

Step 1.1.2

Factor $y$ out of $- 5 y$ .

$\frac{2 y}{y \cdot y + y \cdot - 5} - \frac{- 3 y}{y - 5}$

Step 1.1.3

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

$\frac{2 y}{y (y - 5)} - \frac{- 3 y}{y - 5}$

Step 1.2

Cancel the common factor of $y$ .

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Step 1.2.1

Cancel the common factor.

$\frac{2 y}{y (y - 5)} - \frac{- 3 y}{y - 5}$

Step 1.2.2

Rewrite the expression.

$\frac{2}{y - 5} - \frac{- 3 y}{y - 5}$

Step 1.3

Move the negative in front of the fraction.

$\frac{2}{y - 5} - - \frac{3 y}{y - 5}$

Step 1.4

Multiply $- - \frac{3 y}{y - 5}$ .

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{2}{y - 5} + 1 \frac{3 y}{y - 5}$

Step 1.4.2

Multiply $\frac{3 y}{y - 5}$ by $1$ .

$\frac{2}{y - 5} + \frac{3 y}{y - 5}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 + 3 y}{y - 5}$