Question

1. \\(\frac{2x^2 + 12x - 14}{4x + 28}\\)

Explanation:

Step1: Factor numerator and denominator

Factor numerator \(2x^2 + 12x - 14\): First, factor out 2: \(2(x^2 + 6x - 7)\). Then factor the quadratic: \(2(x + 7)(x - 1)\).
Factor denominator \(4x + 28\): Factor out 4: \(4(x + 7)\).
So the expression becomes \(\frac{2(x + 7)(x - 1)}{4(x + 7)}\).

Step2: Cancel common factors

Cancel out the common factor \((x + 7)\) (assuming \(x
eq -7\)) and simplify the constants: \(\frac{2}{4}=\frac{1}{2}\).
The simplified expression is \(\frac{x - 1}{2}\) (or \(\frac{1}{2}x - \frac{1}{2}\)).

Answer:

\(\boldsymbol{\frac{x - 1}{2}}\) (or \(\boldsymbol{\frac{1}{2}x - \frac{1}{2}}\))