Basic Math Examples

$\frac{3 y + 6}{y^{2} - 3 y + 2} \cdot \frac{y^{2} - y - 2}{y + 2}$

Step 1

Factor $3$ out of $3 y + 6$ .

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Step 1.1

Factor $3$ out of $3 y$ .

$\frac{3 (y) + 6}{y^{2} - 3 y + 2} \cdot \frac{y^{2} - y - 2}{y + 2}$

Step 1.2

Factor $3$ out of $6$ .

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

Step 1.3

Factor $3$ out of $3 y + 3 \cdot 2$ .

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

Step 2

Factor $y^{2} - 3 y + 2$ using the AC method.

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Step 2.1

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 $- 3$ .

$- 2, - 1$

Step 2.2

Write the factored form using these integers.

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

Step 3

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

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Step 3.1

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 $- 1$ .

$- 2, 1$

Step 3.2

Write the factored form using these integers.

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $y + 2$ .

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Step 4.1.1

Factor $y + 2$ out of $3 (y + 2)$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $y - 2$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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

Step 4.3

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

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