Question

1. \\(\frac{v + 1}{15v - 9} - \frac{5}{3}\\)

Explanation:

Step1: Factor the denominator

Factor \(15v - 9\) as \(3(5v - 3)\). So the expression becomes \(\frac{v + 1}{3(5v - 3)}-\frac{5}{3}\).

Step2: Find a common denominator

The common denominator is \(3(5v - 3)\). Rewrite \(\frac{5}{3}\) with the common denominator: \(\frac{5(5v - 3)}{3(5v - 3)}\).

Step3: Subtract the fractions

Subtract the two fractions: \(\frac{v + 1 - 5(5v - 3)}{3(5v - 3)}\).

Step4: Simplify the numerator

Expand and simplify the numerator: \(v + 1 - 25v + 15 = -24v + 16\). Factor out \(-8\) from the numerator: \(-8(3v - 2)\). So the expression is \(\frac{-8(3v - 2)}{3(5v - 3)}\) or \(\frac{8(2 - 3v)}{3(5v - 3)}\).

Answer:

\(\frac{8(2 - 3v)}{3(5v - 3)}\) (or \(\frac{-8(3v - 2)}{3(5v - 3)}\))