Simplify (20x^2+30x)/(4x^4+6x^3)

$\frac{20 x^{2} + 30 x}{4 x^{4} + 6 x^{3}}$

Step 1

Factor $10 x$ out of $20 x^{2} + 30 x$ .

Factor $10 x$ out of $20 x^{2}$ .

$\frac{10 x (2 x) + 30 x}{4 x^{4} + 6 x^{3}}$

Factor $10 x$ out of $30 x$ .

$\frac{10 x (2 x) + 10 x (3)}{4 x^{4} + 6 x^{3}}$

Factor $10 x$ out of $10 x (2 x) + 10 x (3)$ .

$\frac{10 x (2 x + 3)}{4 x^{4} + 6 x^{3}}$

$\frac{10 x (2 x + 3)}{4 x^{4} + 6 x^{3}}$

Step 2

Factor $2 x^{3}$ out of $4 x^{4} + 6 x^{3}$ .

Factor $2 x^{3}$ out of $4 x^{4}$ .

$\frac{10 x (2 x + 3)}{2 x^{3} (2 x) + 6 x^{3}}$

Factor $2 x^{3}$ out of $6 x^{3}$ .

$\frac{10 x (2 x + 3)}{2 x^{3} (2 x) + 2 x^{3} (3)}$

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

$\frac{10 x (2 x + 3)}{2 x^{3} (2 x + 3)}$

$\frac{10 x (2 x + 3)}{2 x^{3} (2 x + 3)}$

Step 3

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 x (2 x + 3)$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $x$ and $x^{3}$ .

Factor $x$ out of $5 x (2 x + 3)$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $2 x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{5}{x^{2}}$

$\frac{5}{x^{2}}$

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