Question

1. \\(\frac{v^2 + 7v - 30}{9v^2 + 90v}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(v^{2}+7v - 30\): find two numbers that multiply to \(-30\) and add to \(7\), which are \(10\) and \(-3\). So \(v^{2}+7v - 30=(v + 10)(v - 3)\).

Factor \(9v^{2}+90v\): take out the common factor \(9v\), so \(9v^{2}+90v = 9v(v + 10)\).

Step2: Simplify the fraction

Now the fraction is \(\frac{(v + 10)(v - 3)}{9v(v + 10)}\). Cancel out the common factor \((v + 10)\) (assuming \(v
eq - 10\) to avoid division by zero).

We get \(\frac{v - 3}{9v}\).

Answer:

\(\frac{v - 3}{9v}\) (for \(v
eq - 10\) and \(v
eq0\))