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QuestionMathematics

Find the difference of the fractions: $\frac{2}{x+ 10}-\frac{3}{x+ 4}$
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Answer

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Step 1:
I'll solve this step by step, carefully following the LaTeX formatting guidelines:

Step 2:
: Identify the Problem

We need to subtract two fractions with different denominators: $$\frac{2}{x+10} - \frac{3}{x+4}

Step 3:
: Find the Least Common Denominator (LCD)

The LCD will be the product of the denominators: $$(x+10)(x+4)

Step 4:
: Rewrite Each Fraction with the LCD

\frac{2}{x+10} = \frac{2(x+4)}{(x+10)(x+4)}
\frac{3}{x+ 4} = \frac{3(x+ 10)}{(x+ 10)(x+ 4)}

Step 5:
: Subtract the Fractions

\frac{2(x+4) - 3(x+10)}{(x+10)(x+4)}

Step 6:
: Simplify the Numerator

\frac{2x + 8 - 3x - 30}{(x+10)(x+4)}
\frac{-x - 22}{(x+ 10)(x+ 4)}

Final Answer

Note: The domain of this expression excludes x = - 10 and x = - 4 to avoid division by zero.