QQuestionMathematics
QuestionMathematics
"Write as a single fraction in its simplest form:
a/b + c/d + e/f"
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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 add three fractions $$\frac{a}{b} + \frac{c}{d} + \frac{e}{f}$$ and express the result as a single simplified fraction.
Step 3:: Find the Least Common Denominator (LCD)
To add fractions, we must find the least common multiple (LCM) of the denominators $$b$$, $$d$$, and $$f$$.
Step 4:: Convert Each Fraction to Have the LCD
\frac{a}{b} \cdot \frac{df}{df} + \frac{c}{d} \cdot \frac{bf}{bf} + \frac{e}{f} \cdot \frac{bd}{bd}
Multiply each fraction by the appropriate factor to get a common denominator:
Step 5:: Rewrite the Equation
\frac{adf}{bdf} + \frac{cbf}{bdf} + \frac{ebd}{bdf}
Step 6:: Add the Numerators
\frac{adf + cbf + ebd}{bdf}
Step 7:: Simplify if Possible
Look for common factors between the numerator and denominator to reduce the fraction.
Final Answer
Note: This is the most general form. The fraction cannot be simplified further without knowing the specific values of a, b, c, d, e, and f.
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