CEMC Fermat, 2015

Algebra Difficulty 2.6 Junior Find the answer Canada

If $a$ and $b$ are two distinct numbers with $\dfrac{a + b}{a - b} = 3$ , then $\dfrac{a}{b}$ equals

Pick one

Solution

Since $\dfrac{a+b}{a-b}=3$ , then $a+b=3(a-b)$ or $a+b=3a-3b$ .

Thus, $4b = 2a$ and so $2b=a$ or $2 = \dfrac{a}{b}$ .

(Note that $b \neq 0$ , since otherwise the original equation would become $\dfrac{a}{a}=3$ , which is not true.)

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