Question:
If $x * y = \frac{1}{x} + \frac{1}{y}$ for all $x,y \in \mathbb{R} - \{0\}$, then $(5 * 2) * (3 * 5) =$ ?
If $x * y = \frac{1}{x} + \frac{1}{y}$ for all $x,y \in \mathbb{R} - \{0\}$, then $(5 * 2) * (3 * 5) =$ ?
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Carefully substitute values in custom operations—don’t treat them as normal multiplication.
Updated On: Apr 23, 2026
- $\frac{185}{64}$
- $\frac{185}{56}$
- $\frac{170}{39}$
- $\frac{145}{82}$
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The Correct Option is B
Solution and Explanation
Concept:
Given operation:
\[
x * y = \frac{1}{x} + \frac{1}{y}
\]
Step 1: Find $5 * 2$.
\[ 5 * 2 = \frac{1}{5} + \frac{1}{2} = \frac{2+5}{10} = \frac{7}{10} \]
Step 2: Find $3 * 5$.
\[ 3 * 5 = \frac{1}{3} + \frac{1}{5} = \frac{5+3}{15} = \frac{8}{15} \]
Step 3: Compute final expression.
\[ \left(\frac{7}{10}\right) * \left(\frac{8}{15}\right) = \frac{10}{7} + \frac{15}{8} \] \[ = \frac{80 + 105}{56} = \frac{185}{56} \]
Hence, the value is $\frac{185{56}$.
Step 1: Find $5 * 2$.
\[ 5 * 2 = \frac{1}{5} + \frac{1}{2} = \frac{2+5}{10} = \frac{7}{10} \]
Step 2: Find $3 * 5$.
\[ 3 * 5 = \frac{1}{3} + \frac{1}{5} = \frac{5+3}{15} = \frac{8}{15} \]
Step 3: Compute final expression.
\[ \left(\frac{7}{10}\right) * \left(\frac{8}{15}\right) = \frac{10}{7} + \frac{15}{8} \] \[ = \frac{80 + 105}{56} = \frac{185}{56} \]
Hence, the value is $\frac{185{56}$.
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