Basic Math Examples

$\frac{y^{2} + y - 2}{y + 3} \cdot \frac{y - 2}{4 y - 4}$

Step 1

Factor $y^{2} + y - 2$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Step 1.2

Write the factored form using these integers.

$\frac{(y - 1) (y + 2)}{y + 3} \cdot \frac{y - 2}{4 y - 4}$

Step 2

Simplify terms.

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Step 2.1

Factor $4$ out of $4 y - 4$ .

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Step 2.1.1

Factor $4$ out of $4 y$ .

$\frac{(y - 1) (y + 2)}{y + 3} \cdot \frac{y - 2}{4 (y) - 4}$

Step 2.1.2

Factor $4$ out of $- 4$ .

$\frac{(y - 1) (y + 2)}{y + 3} \cdot \frac{y - 2}{4 (y) + 4 (- 1)}$

Step 2.1.3

Factor $4$ out of $4 (y) + 4 (- 1)$ .

$\frac{(y - 1) (y + 2)}{y + 3} \cdot \frac{y - 2}{4 (y - 1)}$

Step 2.2

Cancel the common factor of $y - 1$ .

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Step 2.2.1

Factor $y - 1$ out of $4 (y - 1)$ .

$\frac{(y - 1) (y + 2)}{y + 3} \cdot \frac{y - 2}{(y - 1) \cdot 4}$

Step 2.2.2

Cancel the common factor.

$\frac{(y - 1) (y + 2)}{y + 3} \cdot \frac{y - 2}{(y - 1) \cdot 4}$

Step 2.2.3

Rewrite the expression.

$\frac{y + 2}{y + 3} \cdot \frac{y - 2}{4}$

Step 2.3

Multiply $\frac{y + 2}{y + 3}$ by $\frac{y - 2}{4}$ .

$\frac{(y + 2) (y - 2)}{(y + 3) \cdot 4}$

Step 2.4

Move $4$ to the left of $y + 3$ .

$\frac{(y + 2) (y - 2)}{4 (y + 3)}$