CEMC Fermat

Algebra Difficulty 2.1 Junior Find the answer

If $a$ and $b$ are two distinct numbers with $\frac{a+b}{a-b}=3$ , what is the value of $\frac{a}{b}$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $\frac{a+b}{a-b}=3$ , then $a+b=3(a-b)$ or $a+b=3a-3b$ . Thus, $4b=2a$ and so $2b=a$ or $2=\frac{a}{b}$ . (Note that $b \neq 0$ , since otherwise the original equation would become $\frac{a}{a}=3$ , which is not true.)

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