IMAT 2019 Q58 [Equation]

In order to solve this, we will multiply the whole equation with x(x-2). This is possible because neither of them are 0.

We get:
3(x-2) + 2x = x(x-2) \to 3x-6+2x = x^2 -2x \to x^2 -2x -5x +6 =0 \to x^2 -7x +6 =0

We can now either use the formula for x_{1,2} or solve it like this:
x^2 -7x +6 = x^2 -x -6x +6 = x(x-1) -6 (x-1) = (x-1)(x-6) \to (x-1)(x-6) = 0 \to x_1 = 1, x_2 = 6

Adding those together we get the final solution:
x_1 +x_2 = 1+6 = 7 (E)

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