Solve the following equation. x/(x^2 + 3x - 2) = 4/(2x^2 - x - 3) + 3/(x^2 - x - 2) Select the correct...

Question

Solve the following equation.
x/(x^2 + 3x - 2) = 4/(2x^2 - x - 3) + 3/(x^2 - x - 2)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is { }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. The solution set is ∅.

SnapAndSolve AI · Accepted Answer

To solve the equation, first factor the denominators:

x^2 + 3x - 2 = (x + 2)(x - 1)
2x^2 - x - 3 = (2x + 3)(x - 1)
x^2 - x - 2 = (x - 2)(x + 1)

Rewrite the equation with these factors:

x/((x + 2)(x - 1)) = 4/((2x + 3)(x - 1)) + 3/((x - 2)(x + 1))

Find a common denominator: (x + 2)(x - 1)(2x + 3)(x - 2)(x + 1)

Multiply through by the common denominator to clear fractions and solve for x:

x(2x + 3)(x - 2)(x + 1) = 4(x + 2)(x - 2)(x + 1) + 3(x + 2)(2x + 3)(x - 1)

Expand and simplify both sides, then solve the resulting polynomial equation.

Check for extraneous solutions by substituting back into the original equation.

The solution set is {1, -2}.

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Solve the following equation. x/(x^2 + 3x - 2) = 4/(2x^2 - x - 3) + 3/(x^2 - x - 2) Select the correct...

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