# How do you solve the rational equation #(2x)/(x+4)=3/(x-1)#?

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To solve the rational equation (2x)/(x+4)=3/(x-1), you can start by cross-multiplying to eliminate the fractions. This gives you 2x(x-1) = 3(x+4). Expanding and simplifying the equation, you get 2x^2 - 2x = 3x + 12. Rearranging the terms, you have 2x^2 - 5x - 12 = 0. To solve this quadratic equation, you can factor it as (2x + 3)(x - 4) = 0. Setting each factor equal to zero, you find two possible solutions: x = -3/2 and x = 4. Therefore, the solutions to the rational equation are x = -3/2 and x = 4.

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