Answer
$F$
Work Step by Step
Subtract the fractions in the numerator and denominator first.
Find the least common denominator, LCD, which incorporates all factors in the denominators of the two fractions. Multiply the numerator in each fraction by the factor that is missing between its denominator and the LCD:
$\frac{\frac{3(x)}{x} - \frac{1}{x}}{\frac{1}{2x} - \frac{5(2x)}{2x}}$
Simplify:
$\frac{\frac{3x}{x} - \frac{1}{x}}{\frac{1}{2x} - \frac{10x}{2x}}$
Subtract the two fractions in the numerator and the denominator:
$\frac{\frac{3x - 1}{x}}{\frac{1 - 10x}{2x}}$
Rewrite the exercise using the division ($\div$) symbol:
$\frac{3x - 1}{x} \div \frac{1 - 10x}{2x}$
To divide one rational expression by another, multiply the first expression by the reciprocal of the second:
$\frac{3x - 1}{x} \bullet \frac{2x}{1 - 10x}$
Cancel common terms in the numerator and denominator:
$\frac{2(3x - 1)}{1 - 10x}$
Simplify:
$\frac{6x - 2}{1 - 10x}$
This answer corresponds to option $F$.
