Question : If $\frac{a}{b} = \frac{7}{6}$, find the value of the expression $\frac{6a + 13b}{6a – 13b}$.
Option 1: $–\frac{3}{10}$
Option 2: $\frac{10}{3}$
Option 3: $–\frac{10}{3}$
Option 4: $\frac{3}{10}$
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Correct Answer: $–\frac{10}{3}$
Solution : Given: $\frac{a}{b} = \frac{7}{6}$ $\frac{6a + 13b}{6a – 13b}$ Divide the numerator and denominator of the above expression by b. $=\frac{6 \times\frac{a}{b} +13}{6 \times\frac{a}{b} – 13 }$ Substitute the value of $\frac{a}{b} = \frac{7}{6}$ in the expression. $=\frac{6 \times\frac{7}{6} + 13 }{6 \times\frac{7}{6} – 13 }$ $=\frac{7+13 }{7 – 13 }$ $= –\frac{10}{3 }$ Hence, the correct answer is $–\frac{10}{3 }$.
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