Simplify (4(1/x)+3)/(6(1/x)+2)

$\frac{4 (\frac{1}{x}) + 3}{6 (\frac{1}{x}) + 2}$

Step 1

Simplify the numerator.

Combine $4$ and $\frac{1}{x}$ .

$\frac{\frac{4}{x} + 3}{6 \frac{1}{x} + 2}$

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

$\frac{\frac{4}{x} + \frac{3 x}{x}}{6 \frac{1}{x} + 2}$

Combine the numerators over the common denominator.

$\frac{\frac{4 + 3 x}{x}}{6 \frac{1}{x} + 2}$

Step 2

Simplify the denominator.

Factor $2$ out of $6 \frac{1}{x} + 2$ .

Factor $2$ out of $6 \frac{1}{x}$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (3 \frac{1}{x}) + 2 (1)$ .

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

Combine $3$ and $\frac{1}{x}$ .

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Step 3

Combine $2$ and $\frac{3 + x}{x}$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Multiply $4 + 3 x$ by $\frac{1}{2 (3 + x)}$ .

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