Question

subtract the rational expressions and write the answer in simplest form. $\frac{x - 4}{x + 5}-\frac{x}{2x + 10}$ $\frac{2x - 4}{x + 5}$ $\frac{-3x^{2}-7x - 40}{2x + 5}$ $\frac{x - 8}{2x + 10}$ $\frac{-4}{3x + 15}$

Explanation:

Step1: Factor the denominator

Factor \(2x + 10\) as \(2(x + 5)\). So the expression is \(\frac{x - 4}{x + 5}-\frac{x}{2(x + 5)}\).

Step2: Find a common - denominator

The common denominator of \(x + 5\) and \(2(x + 5)\) is \(2(x + 5)\). Rewrite \(\frac{x - 4}{x + 5}\) as \(\frac{2(x - 4)}{2(x + 5)}=\frac{2x-8}{2(x + 5)}\).

Step3: Subtract the numerators

\(\frac{2x-8}{2(x + 5)}-\frac{x}{2(x + 5)}=\frac{2x - 8-x}{2(x + 5)}\).

Step4: Simplify the numerator

Combine like - terms in the numerator: \(2x-8 - x=x - 8\). So the result is \(\frac{x - 8}{2(x + 5)}=\frac{x - 8}{2x+10}\).

Answer:

\(\frac{x - 8}{2x + 10}\)