Algebra Examples

$\frac{3 x^{2} + 13 x + 4}{(\frac{3 x + 1}{5})}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(3 x^{2} + 13 x + 4) \frac{5}{3 x + 1}$

Step 2

Multiply $3 x^{2} + 13 x + 4$ by $\frac{5}{3 x + 1}$ .

$\frac{(3 x^{2} + 13 x + 4) \cdot 5}{3 x + 1}$

Step 3

Factor by grouping.

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Step 3.1

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 $a \cdot c = 3 \cdot 4 = 12$ and whose sum is $b = 13$ .

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Step 3.1.1

Factor $13$ out of $13 x$ .

$\frac{(3 x^{2} + 13 (x) + 4) \cdot 5}{3 x + 1}$

Step 3.1.2

Rewrite $13$ as $1$ plus $12$

$\frac{(3 x^{2} + (1 + 12) x + 4) \cdot 5}{3 x + 1}$

Step 3.1.3

Apply the distributive property.

$\frac{(3 x^{2} + 1 x + 12 x + 4) \cdot 5}{3 x + 1}$

Step 3.1.4

Multiply $x$ by $1$ .

$\frac{(3 x^{2} + x + 12 x + 4) \cdot 5}{3 x + 1}$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$\frac{((3 x^{2} + x) + 12 x + 4) \cdot 5}{3 x + 1}$

Step 3.2.2

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

$\frac{(x (3 x + 1) + 4 (3 x + 1)) \cdot 5}{3 x + 1}$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$\frac{(3 x + 1) (x + 4) \cdot 5}{3 x + 1}$

Step 4

Cancel the common factor of $3 x + 1$ .

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Step 4.1

Cancel the common factor.

$\frac{(3 x + 1) (x + 4) \cdot 5}{3 x + 1}$

Step 4.2

Divide $(x + 4) \cdot 5$ by $1$ .

$(x + 4) \cdot 5$

Step 5

Apply the distributive property.

$x \cdot 5 + 4 \cdot 5$

Step 6

Simplify the expression.

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Step 6.1

Move $5$ to the left of $x$ .

$5 \cdot x + 4 \cdot 5$

Step 6.2

Multiply $4$ by $5$ .

$5 x + 20$