Pre-Algebra Examples

$\frac{6 x^{2} + 5 x - 1}{6 x + 6}$

Step 1

Factor by grouping.

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Step 1.1

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 $a \cdot c = 6 \cdot - 1 = - 6$ and whose sum is $b = 5$ .

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Step 1.1.1

Factor $5$ out of $5 x$ .

$\frac{6 x^{2} + 5 (x) - 1}{6 x + 6}$

Step 1.1.2

Rewrite $5$ as $- 1$ plus $6$

$\frac{6 x^{2} + (- 1 + 6) x - 1}{6 x + 6}$

Step 1.1.3

Apply the distributive property.

$\frac{6 x^{2} - 1 x + 6 x - 1}{6 x + 6}$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$\frac{(6 x^{2} - 1 x) + 6 x - 1}{6 x + 6}$

Step 1.2.2

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

$\frac{x (6 x - 1) + 1 (6 x - 1)}{6 x + 6}$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $6 x - 1$ .

$\frac{(6 x - 1) (x + 1)}{6 x + 6}$

Step 2

Factor $6$ out of $6 x + 6$ .

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Step 2.1

Factor $6$ out of $6 x$ .

$\frac{(6 x - 1) (x + 1)}{6 (x) + 6}$

Step 2.2

Factor $6$ out of $6$ .

$\frac{(6 x - 1) (x + 1)}{6 (x) + 6 (1)}$

Step 2.3

Factor $6$ out of $6 (x) + 6 (1)$ .

$\frac{(6 x - 1) (x + 1)}{6 (x + 1)}$

Step 3

Cancel the common factor of $x + 1$ .

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Step 3.1

Cancel the common factor.

$\frac{(6 x - 1) (x + 1)}{6 (x + 1)}$

Step 3.2

Rewrite the expression.

$\frac{6 x - 1}{6}$

Step 4

Split the fraction $\frac{6 x - 1}{6}$ into two fractions.

$\frac{6 x}{6} + \frac{- 1}{6}$

Step 5

Cancel the common factor of $6$ .

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Step 5.1

Cancel the common factor.

$\frac{6 x}{6} + \frac{- 1}{6}$

Step 5.2

Divide $x$ by $1$ .

$x + \frac{- 1}{6}$

Step 6

Move the negative in front of the fraction.

$x - \frac{1}{6}$