Question

select the correct answer.

assuming no denominator equals zero, which expression is equivalent to the given expression?

\\\frac{\frac{r - 5}{9r}}{\frac{5 - r}{3r^2}}\\

• \\(-\frac{3}{r}\\)
• \\(\frac{r}{3}\\)
• \\(-\frac{r}{3}\\)
• \\(\frac{r - 5}{5 - 3r}\\)

Explanation:

Write the complex fraction expression

$$ \frac{\frac{r - 5}{9r}}{\frac{5 - r}{3r^2}} $$

Multiply by the reciprocal of the denominator

$$ \frac{r - 5}{9r} \cdot \frac{3r^2}{5 - r} $$

Simplify the factors and terms

$$
LATEXBLOCK0
$$

Answer:

• (A) \(-\frac{3}{r}\)
• (B) \(\frac{r}{3}\)
• (C) \(-\frac{r}{3}\) (Correct answer)
• (D) \(\frac{r - 5}{5 - 3r}\)