Solve the rational equation (frac{2x^2 - 3x - 2}{x^2 - x - 6} = frac{4x - 3}{x + 1})

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Accepted Answer

Step:1 ：Step 1: Factor the polynomials in the equation. We get (frac{2(x - 1)(x + 2)}{(x - 2)(x + 3)} = frac{4(x - frac{3}{4})}{x + 1})Step:2 ：Step 2: Cross multiply the denominators, we get (2(x - 1)(x + 2)(x + 1) = 4(x - frac{3}{4})(x - 2)(x + 3))Step:3 ：Step 3: Simplify the equation and set it to zero, we get (2x^3 + x^2 - 6x - 4 = 4x^3 - frac{3x^2}{2} - frac{21x}{2} + 6)Step:4 ：Step 4: Collect like terms and simplify the equation, we get (2x^3 - 4x^3 + x^2 + frac{3x^2}{2} + 6x + frac{21x}{2} - 4 - 6 = 0)Step:5 ：Step 5: Simplify further to get (-2x^3 + frac{5x^2}{2} + frac{27x}{2} = 0)Step:6 ：Step 6: Factor the equation to find the roots, we get (-2x(x - 3)(x + frac{9}{2}) = 0)Step:7 ：Step 7: So, the solutions are (x = 0, x = 3, x = -frac{9}{2})

Answer

Step: 1 ：Step 1: Factor the polynomials in the equation. We get (frac{2(x - 1)(x + 2)}{(x - 2)(x + 3)} = frac{4(x - frac{3}{4})}{x + 1})Step: 2 ：Step 2: Cross multiply the denominators, we get (2(x - 1)(x + 2)(x + 1) = 4(x - frac{3}{4})(x - 2)(x + 3))Step: 3 ：Step 3: Simplify the equation and set it to zero, we get (2x^3 + x^2 - 6x - 4 = 4x^3 - frac{3x^2}{2} - frac{21x}{2} + 6)Step: 4 ：Step 4: Collect like terms and simplify the equation, we get (2x^3 - 4x^3 + x^2 + frac{3x^2}{2} + 6x + frac{21x}{2} - 4 - 6 = 0)Step: 5 ：Step 5: Simplify further to get (-2x^3 + frac{5x^2}{2} + frac{27x}{2} = 0)Step: 6 ：Step 6: Factor the equation to find the roots, we get (-2x(x - 3)(x + frac{9}{2}) = 0)Step: 7 ：Step 7: So, the solutions are (x = 0, x = 3, x = -frac{9}{2})

Solve the rational equation $\frac{2 x^{2} - 3 x - 2}{x^{2} - x - 6} = \frac{4 x - 3}{x + 1}$

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Popular Problems

Solve the rational equation 2x2−3x−2x2−x−6=4x−3x+1

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Popular Problems

Solve the rational equation $\frac{2 x^{2} - 3 x - 2}{x^{2} - x - 6} = \frac{4 x - 3}{x + 1}$