Basic Math Examples

$\frac{c - y}{c^{2} + y} \cdot \frac{c^{2}}{y^{2} - c y}$

Step 1

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

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Step 1.1

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

$\frac{c - y}{c^{2} + y} \cdot \frac{c^{2}}{y \cdot y - c y}$

Step 1.2

Factor $y$ out of $- c y$ .

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

Step 1.3

Factor $y$ out of $y \cdot y + y (- c)$ .

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

Step 2

Multiply $\frac{c - y}{c^{2} + y}$ by $\frac{c^{2}}{y (y - c)}$ .

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

Step 3

Cancel the common factor of $c - y$ and $y - c$ .

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Step 3.1

Factor $- 1$ out of $c$ .

$\frac{(- 1 (- c) - y) c^{2}}{(c^{2} + y) (y (y - c))}$

Step 3.2

Factor $- 1$ out of $- y$ .

$\frac{(- 1 (- c) - (y)) c^{2}}{(c^{2} + y) (y (y - c))}$

Step 3.3

Factor $- 1$ out of $- 1 (- c) - (y)$ .

$\frac{- 1 (- c + y) c^{2}}{(c^{2} + y) (y (y - c))}$

Step 3.4

Reorder terms.

$\frac{- 1 (- c + y) c^{2}}{(c^{2} + y) y (- c + y)}$

Step 3.5

Cancel the common factor.

$\frac{- 1 (- c + y) c^{2}}{(c^{2} + y) y (- c + y)}$

Step 3.6

Rewrite the expression.

$\frac{- 1 c^{2}}{(c^{2} + y) y}$

Step 4

Simplify the expression.

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Step 4.1

Move the negative in front of the fraction.

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

Step 4.2

Reorder factors in $- \frac{c^{2}}{(c^{2} + y) y}$ .

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