Question

simplify.
\\(\dfrac{7 + \dfrac{3}{w}}{5 + \dfrac{3}{w}}\\)

Explanation:

Step1: Simplify numerator and denominator separately

For the numerator \(7 + \frac{3}{w}\), find a common denominator \(w\): \(7 + \frac{3}{w}=\frac{7w}{w}+\frac{3}{w}=\frac{7w + 3}{w}\)
For the denominator \(5+\frac{3}{w}\), find a common denominator \(w\): \(5+\frac{3}{w}=\frac{5w}{w}+\frac{3}{w}=\frac{5w + 3}{w}\)

Step2: Divide the simplified numerator by the simplified denominator

The original expression becomes \(\frac{\frac{7w + 3}{w}}{\frac{5w + 3}{w}}\). When dividing by a fraction, multiply by its reciprocal: \(\frac{7w + 3}{w}\times\frac{w}{5w + 3}\)

Step3: Cancel out the common factor \(w\)

The \(w\) in the numerator and denominator cancels, leaving \(\frac{7w + 3}{5w + 3}\)

Answer:

\(\frac{7w + 3}{5w + 3}\)