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What is the sum? x/x+ 3 + 3 /x+ 3 + 2 /x+ 3 A) 5 / 3 B) x+ 5 /x+ 3 C) x+ 5 / 3x+ 27 D) 6x/x+ 3
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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 given expression

The expression is $$\frac{x}{x+3} + \frac{3}{x+3} + \frac{2}{x+3}

Step 3:
: Find a common denominator

Note that all terms already have the same denominator $$x+3$$, which simplifies our addition.

Step 4:
: Add the numerators

\frac{x}{x+3} + \frac{3}{x+3} + \frac{2}{x+3} = \frac{x + 3 + 2}{x+3}

Step 5:
: Simplify the numerator

\frac{x + 5}{x+3}

Step 6:
: Verify the result

This matches option B: $$\frac{x+5}{x+3}

Final Answer

Key insights: - The common denominator allows direct addition of numerators - The result simplifies to \frac{x+ 5}{x+ 3} - Note that this is valid for all values of x where x+ 3 \neq 0