Simplify (2x^2+x)/(2x^3+7x^2+3x)

$\frac{2 x^{2} + x}{2 x^{3} + 7 x^{2} + 3 x}$

Step 1

Factor $x$ out of $2 x^{2} + x$ .

Factor $x$ out of $2 x^{2}$ .

$\frac{x (2 x) + x}{2 x^{3} + 7 x^{2} + 3 x}$

Raise $x$ to the power of $1$ .

$\frac{x (2 x) + x^{1}}{2 x^{3} + 7 x^{2} + 3 x}$

Factor $x$ out of $x^{1}$ .

$\frac{x (2 x) + x \cdot 1}{2 x^{3} + 7 x^{2} + 3 x}$

Factor $x$ out of $x (2 x) + x \cdot 1$ .

$\frac{x (2 x + 1)}{2 x^{3} + 7 x^{2} + 3 x}$

Step 2

Simplify the denominator.

Factor $x$ out of $2 x^{3} + 7 x^{2} + 3 x$ .

Factor $x$ out of $2 x^{3}$ .

$\frac{x (2 x + 1)}{x (2 x^{2}) + 7 x^{2} + 3 x}$

Factor $x$ out of $7 x^{2}$ .

$\frac{x (2 x + 1)}{x (2 x^{2}) + x (7 x) + 3 x}$

Factor $x$ out of $3 x$ .

$\frac{x (2 x + 1)}{x (2 x^{2}) + x (7 x) + x \cdot 3}$

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

$\frac{x (2 x + 1)}{x (2 x^{2} + 7 x) + x \cdot 3}$

Factor $x$ out of $x (2 x^{2} + 7 x) + x \cdot 3$ .

$\frac{x (2 x + 1)}{x (2 x^{2} + 7 x + 3)}$

Factor by grouping.

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 $a \cdot c = 2 \cdot 3 = 6$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{x (2 x + 1)}{x (2 x^{2} + 7 (x) + 3)}$

Rewrite $7$ as $1$ plus $6$

$\frac{x (2 x + 1)}{x (2 x^{2} + (1 + 6) x + 3)}$

Apply the distributive property.

$\frac{x (2 x + 1)}{x (2 x^{2} + 1 x + 6 x + 3)}$

Multiply $x$ by $1$ .

$\frac{x (2 x + 1)}{x (2 x^{2} + x + 6 x + 3)}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{x (2 x + 1)}{x ((2 x^{2} + x) + 6 x + 3)}$

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

$\frac{x (2 x + 1)}{x (x (2 x + 1) + 3 (2 x + 1))}$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$\frac{x (2 x + 1)}{x ((2 x + 1) (x + 3))}$

$\frac{x (2 x + 1)}{x (2 x + 1) (x + 3)}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (2 x + 1)}{x (2 x + 1) (x + 3)}$

Rewrite the expression.

$\frac{2 x + 1}{(2 x + 1) (x + 3)}$

Cancel the common factor of $2 x + 1$ .

Cancel the common factor.

$\frac{2 x + 1}{(2 x + 1) (x + 3)}$

Rewrite the expression.

$\frac{1}{x + 3}$

Simplify (2x^2+x)/(2x^3+7x^2+3x)

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