Let's divide the fractions and simplify the expression step by step. The given problem is:
\[ \frac{\frac{7}{x} + \frac{2}{9}}{3x + 6} \]
First, let's simplify the expression inside the fraction:
\[ \frac{7}{x} + \frac{2}{9} \]
To add these fractions, we need a common denominator. The common denominator for \( \frac{7}{x} \) and \( \frac{2}{9} \) is \( 9x \):
\[ \frac{7}{x} = \frac{7 \cdot 9}{9 \cdot x} = \frac{63}{9x} \]
\[ \frac{2}{9} = \frac{2 \cdot x}{9 \cdot x} = \frac{2x}{9x} \]
Now, add the fractions:
\[ \frac{63}{9x} + \frac{2x}{9x} = \frac{63 + 2x}{9x} \]
So, the numerator becomes \( \frac{63 + 2x}{9x} \).
Next, simplify the denominator \( 3x + 6 \):
\[ 3x + 6 = 3(x + 2) \]
Now we have:
\[ \frac{\frac{63 + 2x}{9x}}{3(x + 2)} \]
To divide by a fraction, we multiply by the reciprocal:
\[ \frac{63 + 2x}{9x} \times \frac{1}{3(x + 2)} = \frac{63 + 2x}{9x} \times \frac{1}{3(x + 2)} \]
\[ = \frac{63 + 2x}{27x(x + 2)} \]
Given that none of the provided options appear to be a straightforward match to this result, I'll re-examine any potential simplification issues or misunderstandings:
Since the provided options are:
A. \(\frac{7}{9}\)
B. \(7\)
C. \(21\)
D. \(\frac{7}{3}\)
E. \(\frac{63}{4x+8}\)
Upon reviewing the answers, none directly correlate to the simplified form. Double-checking the original problem might be necessary to confirm there are no alternate interpretations.
If around-choice mismatch persists and there are no algebra errors found, it suggests a possible misinterpretation or wrong-answer subset:
None of the above simplified forms (though mathematically consistent) present direct matches. Reviewing also if options better reform are correct.
divide these fractions and select the simplified answer.
7/x+2/9/3x+6
A. 7/9
B. 7
C. 21
D. 7/3
E. 63/4x+8
1 answer