Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

If $\frac{x-y}{x+y}=5$ , what is the value of $\frac{2x+3y}{3x-2y}$ ?

Your answer

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

Solution

Since $\frac{x-y}{x+y}=5$ , then $x-y=5(x+y)$ . This means that $x-y=5x+5y$ and so $0=4x+6y$ or $2x+3y=0$ . Therefore, $\frac{2x+3y}{3x-2y}=\frac{0}{3x-2y}=0$ .

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