divide these fractions and select the simplified answer.

Question

7/x+2/9/3x+6
A. 7/9
B. 7
C. 21
D. 7/3
E. 63/4x+8

Answer 1

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.