Basic Math Examples

$\frac{y^{2} - 5 y + 6}{y^{2} - 4}$

Step 1

Factor $y^{2} - 5 y + 6$ 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 $6$ and whose sum is $- 5$ .

$- 3, - 2$

Step 1.2

Write the factored form using these integers.

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

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

Step 3

Cancel the common factor of $y - 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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