Answer
$\frac{2}{3}$
Work Step by Step
Step 1: $\frac{4+\frac{2}{x}}{6+\frac{3}{x}}$
Step 2: $\frac{(4\times\frac{x}{x})+(\frac{2}{x}\times\frac{1}{1})}{(6\times\frac{x}{x})+(\frac{3}{x}\times\frac{1}{1})}$
Step 3: $\frac{\frac{4x}{x}+\frac{2}{x}}{\frac{6x}{x}+\frac{3}{x}}$
Step 4: $\frac{\frac{4x+2}{x}}{\frac{6x+3}{x}}$
Step 5: $\frac{4x+2}{x}\div\frac{6x+3}{x}$
Step 6: $\frac{4x+2}{x}\times\frac{x}{6x+3}$
Step 7: $\frac{4x+2}{6x+3}$
Step 8: $\frac{2(2x+1)}{3(2x+1)}$
Step 9: $\frac{2}{3}$
