Question

1. \\(\frac{56 - 7x}{x^2 - 13x + 40}\\)

Explanation:

Step1: Factor numerator and denominator

Factor numerator: \(56 - 7x = -7(x - 8)\)
Factor denominator: \(x^2 - 13x + 40\). Find two numbers that multiply to \(40\) and add to \(-13\): \(-5\) and \(-8\). So, \(x^2 - 13x + 40=(x - 5)(x - 8)\)

Step2: Simplify the fraction

Cancel common factor \((x - 8)\) (assuming \(x
eq8\)):
\(\frac{-7(x - 8)}{(x - 5)(x - 8)}=\frac{-7}{x - 5}\) or \(\frac{7}{5 - x}\)

Answer:

\(\boldsymbol{\frac{-7}{x - 5}}\) (or \(\boldsymbol{\frac{7}{5 - x}}\))