Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
adding and subtracting rational expressions
adding and subtracting rational expressions with unlike denominators
find the difference:
\\(\frac{2}{x + 10} - \frac{3}{x + 4}\\)
options:
\\(-\frac{1}{6}\\)
\\(\frac{-x - 22}{(x + 10)(x + 4)}\\)
\\(\frac{-x + 38}{(x + 10)(x + 4)}\\)

Explanation:

Step1: Find a common denominator

The denominators are \(x + 10\) and \(x + 4\). The common denominator is \((x + 10)(x + 4)\).
Rewrite each fraction with the common denominator:
\(\frac{2}{x + 10}=\frac{2(x + 4)}{(x + 10)(x + 4)}\)
\(\frac{3}{x + 4}=\frac{3(x + 10)}{(x + 10)(x + 4)}\)

Step2: Subtract the fractions

Now subtract the two fractions:

$$
LATEXBLOCK0
$$

Answer:

\(\frac{-x - 22}{(x + 10)(x + 4)}\)