Basic Math Examples

$\frac{4 y^{2} + 14 y - 30}{y + 5}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $2$ out of $4 y^{2} + 14 y - 30$ .

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Step 1.1.1

Factor $2$ out of $4 y^{2}$ .

$\frac{2 (2 y^{2}) + 14 y - 30}{y + 5}$

Step 1.1.2

Factor $2$ out of $14 y$ .

$\frac{2 (2 y^{2}) + 2 (7 y) - 30}{y + 5}$

Step 1.1.3

Factor $2$ out of $- 30$ .

$\frac{2 (2 y^{2}) + 2 (7 y) + 2 (- 15)}{y + 5}$

Step 1.1.4

Factor $2$ out of $2 (2 y^{2}) + 2 (7 y)$ .

$\frac{2 (2 y^{2} + 7 y) + 2 (- 15)}{y + 5}$

Step 1.1.5

Factor $2$ out of $2 (2 y^{2} + 7 y) + 2 (- 15)$ .

$\frac{2 (2 y^{2} + 7 y - 15)}{y + 5}$

Step 1.2

Factor by grouping.

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Step 1.2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = 7$ .

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Step 1.2.1.1

Factor $7$ out of $7 y$ .

$\frac{2 (2 y^{2} + 7 (y) - 15)}{y + 5}$

Step 1.2.1.2

Rewrite $7$ as $- 3$ plus $10$

$\frac{2 (2 y^{2} + (- 3 + 10) y - 15)}{y + 5}$

Step 1.2.1.3

Apply the distributive property.

$\frac{2 (2 y^{2} - 3 y + 10 y - 15)}{y + 5}$

Step 1.2.2

Factor out the greatest common factor from each group.

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Step 1.2.2.1

Group the first two terms and the last two terms.

$\frac{2 ((2 y^{2} - 3 y) + 10 y - 15)}{y + 5}$

Step 1.2.2.2

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

$\frac{2 (y (2 y - 3) + 5 (2 y - 3))}{y + 5}$

Step 1.2.3

Factor the polynomial by factoring out the greatest common factor, $2 y - 3$ .

$\frac{2 ((2 y - 3) (y + 5))}{y + 5}$

$\frac{2 (2 y - 3) (y + 5)}{y + 5}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y + 5$ .

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Step 2.1.1

Cancel the common factor.

$\frac{2 (2 y - 3) (y + 5)}{y + 5}$

Step 2.1.2

Divide $2 (2 y - 3)$ by $1$ .

$2 (2 y - 3)$

Step 2.2

Apply the distributive property.

$2 (2 y) + 2 \cdot - 3$

Step 2.3

Multiply.

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Step 2.3.1

Multiply $2$ by $2$ .

$4 y + 2 \cdot - 3$

Step 2.3.2

Multiply $2$ by $- 3$ .

$4 y - 6$