Simplify (3x)/(4x)+(3x)/(x^2)

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

Step 1

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $3 x$ .

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

Cancel the common factors.

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

$\frac{3}{4} + \frac{x \cdot 3}{x \cdot x}$

Cancel the common factor.

$\frac{3}{4} + \frac{x \cdot 3}{x \cdot x}$

Rewrite the expression.

$\frac{3}{4} + \frac{3}{x}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3}{4} \cdot \frac{x}{x} + \frac{3}{x}$

Step 3

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} \cdot \frac{x}{x} + \frac{3}{x} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{x}{x}$ .

$\frac{3 x}{4 x} + \frac{3}{x} \cdot \frac{4}{4}$

Multiply $\frac{3}{x}$ by $\frac{4}{4}$ .

$\frac{3 x}{4 x} + \frac{3 \cdot 4}{x \cdot 4}$

Reorder the factors of $x \cdot 4$ .

$\frac{3 x}{4 x} + \frac{3 \cdot 4}{4 x}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 x + 3 \cdot 4}{4 x}$

Step 6

Factor $3$ out of $3 x + 3 \cdot 4$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $3 \cdot 4$ .

$\frac{3 (x) + 3 (4)}{4 x}$

Factor $3$ out of $3 (x) + 3 (4)$ .

$\frac{3 (x + 4)}{4 x}$