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 these two fractions: $$\frac{2}{x+10} - \frac{3}{x+4}
Step 3:: Find the Least Common Denominator (LCD)
The LCD will be the product of the denominators: $$(x+10)(x+4)
Step 4:: Rewrite Fractions with the LCD
\frac{2(x+4)}{(x+10)(x+4)} - \frac{3(x+10)}{(x+10)(x+4)}
Step 5:: Simplify the Numerators
\frac{2(x+4) - 3(x+10)}{(x+10)(x+4)}
Step 6:: Expand the Numerator
\frac{2x + 8 - 3x - 30}{(x+10)(x+4)}
Step 7:: Combine Like Terms in Numerator
\frac{-x - 22}{(x+10)(x+4)}
Final Answer
Note: This solution is valid for all values of x where x \neq - 10 and x \neq - 4 to avoid division by zero.
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