Question

simplify.
\\(\dfrac{3 - \dfrac{5}{2x}}{7 - \dfrac{5}{2x}}\\)

Explanation:

Step1: Simplify numerator and denominator separately

For the numerator \(3 - \frac{5}{2x}\), find a common denominator \(2x\):
\(3=\frac{6x}{2x}\), so \(3 - \frac{5}{2x}=\frac{6x}{2x}-\frac{5}{2x}=\frac{6x - 5}{2x}\)

For the denominator \(7 - \frac{5}{2x}\), find a common denominator \(2x\):
\(7=\frac{14x}{2x}\), so \(7 - \frac{5}{2x}=\frac{14x}{2x}-\frac{5}{2x}=\frac{14x - 5}{2x}\)

Step2: Divide the simplified numerator by the simplified denominator

The original expression becomes \(\frac{\frac{6x - 5}{2x}}{\frac{14x - 5}{2x}}\)

When dividing by a fraction, multiply by its reciprocal: \(\frac{6x - 5}{2x}\times\frac{2x}{14x - 5}\)

The \(2x\) terms cancel out: \(\frac{6x - 5}{14x - 5}\)

Answer:

\(\frac{6x - 5}{14x - 5}\)