QQuestionMathematics
QuestionMathematics
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
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