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Algebra Difficulty 2.2 Junior Find the answer

If x−yx+y=5\frac{x-y}{x+y}=5, what is the value of 2x+3y3x−2y\frac{2x+3y}{3x-2y}?

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since x−yx+y=5\frac{x-y}{x+y}=5, then x−y=5(x+y)x-y=5(x+y). This means that x−y=5x+5yx-y=5x+5y and so 0=4x+6y0=4x+6y or 2x+3y=02x+3y=0. Therefore, 2x+3y3x−2y=03x−2y=0\frac{2x+3y}{3x-2y}=\frac{0}{3x-2y}=0.

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