Basic Math Examples

$\frac{x y - 5 x + 3 y - 15}{x y + 4 x + 3 y + 12}$

Step 1

Simplify the numerator.

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Step 1.1

Factor out the greatest common factor from each group.

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Step 1.1.1

Group the first two terms and the last two terms.

$\frac{(x y - 5 x) + 3 y - 15}{x y + 4 x + 3 y + 12}$

Step 1.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{x (y - 5) + 3 (y - 5)}{x y + 4 x + 3 y + 12}$

Step 1.2

Factor the polynomial by factoring out the greatest common factor, $y - 5$ .

$\frac{(y - 5) (x + 3)}{x y + 4 x + 3 y + 12}$

Step 2

Simplify the denominator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

$\frac{(y - 5) (x + 3)}{(x y + 4 x) + 3 y + 12}$

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{(y - 5) (x + 3)}{x (y + 4) + 3 (y + 4)}$

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $y + 4$ .

$\frac{(y - 5) (x + 3)}{(y + 4) (x + 3)}$

Step 3

Cancel the common factor of $x + 3$ .

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Step 3.1

Cancel the common factor.

$\frac{(y - 5) (x + 3)}{(y + 4) (x + 3)}$

Step 3.2

Rewrite the expression.

$\frac{y - 5}{y + 4}$