Simplify 9/(3x)-4/(2x^2)

$\frac{9}{3 x} - \frac{4}{2 x^{2}}$

Step 1

Simplify each term.

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9$ .

$\frac{3 \cdot 3}{3 x} - \frac{4}{2 x^{2}}$

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{3 \cdot 3}{3 (x)} - \frac{4}{2 x^{2}}$

Cancel the common factor.

$\frac{3 \cdot 3}{3 x} - \frac{4}{2 x^{2}}$

Rewrite the expression.

$\frac{3}{x} - \frac{4}{2 x^{2}}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

$\frac{3}{x} - \frac{2 \cdot 2}{2 x^{2}}$

Cancel the common factors.

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

$\frac{3}{x} - \frac{2 \cdot 2}{2 (x^{2})}$

Cancel the common factor.

$\frac{3}{x} - \frac{2 \cdot 2}{2 x^{2}}$

Rewrite the expression.

$\frac{3}{x} - \frac{2}{x^{2}}$

Step 2

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3}{x} \cdot \frac{x}{x} - \frac{2}{x^{2}}$

Step 3

Write each expression with a common denominator of $x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{x}$ by $\frac{x}{x}$ .

$\frac{3 x}{x \cdot x} - \frac{2}{x^{2}}$

Multiply $x$ by $x$ .

$\frac{3 x}{x^{2}} - \frac{2}{x^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x - 2}{x^{2}}$