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If $\dfrac{a}{b} = \dfrac{3}{5}$, find the value of $\dfrac{a+b}{a-b}$.
A$4$
B$-4$
C$\dfrac{8}{2}$
D$-2$
Answer & Solution
Correct answer: B. $-4$
By the componendo-dividendo identity, if $\dfrac{a}{b} = \dfrac{c}{d}$ then $\dfrac{a+b}{a-b} = \dfrac{c+d}{c-d}$.
Plug in $c = 3, d = 5$: $\dfrac{3+5}{3-5} = \dfrac{8}{-2} = -4$.
A common slip is to drop the sign and pick option C; pay attention to $a < b$, which forces a negative denominator.
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