Questions: Simplify the complex fraction. [ (r^2/(2 r-5))/(13 r/(8 r-20))=square ]

$Simplify the complex fraction. [ (r^2/(2 r-5))/(13 r/(8 r-20))=square ]$

Transcript text: Simplify the complex fraction. \[ \frac{\frac{r^{2}}{2 r-5}}{\frac{13 r}{8 r-20}}=\square \]

Solution

Step 1: Identify the complex fraction

The given complex fraction is: \[ \frac{\frac{2r - 5}{13r}}{8r - 20} \]

Step 2: Simplify the denominator

Factor out the common factor in the denominator $8r - 20$: \[ 8r - 20 = 4(2r - 5) \]

Step 3: Rewrite the complex fraction

Rewrite the complex fraction using the simplified denominator: \[ \frac{\frac{2r - 5}{13r}}{4(2r - 5)} \]

Step 4: Simplify the complex fraction

Since $\frac{2r - 5}{4(2r - 5)}$ simplifies to $\frac{1}{4}$, the complex fraction becomes: \[ \frac{1}{13r \cdot 4} = \frac{1}{52r} \]

\[ \frac{1}{52r} \]

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