Simplify the rational expression ( frac{2x^2 - 5x - 3}{x^2 - 4} )

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Accepted Answer

Step:1 ：First, we factor the numerator and denominator. The numerator factors to (2x^2 - 5x - 3 = (2x + 1)(x - 3)) and the denominator factors to (x^2 - 4 = (x - 2)(x + 2))Step:2 ：So, our expression becomes ( frac{(2x + 1)(x - 3)}{(x - 2)(x + 2)} )Step:3 ：We cannot simplify this any further because none of the factors in the numerator are the same as the factors in the denominator. Therefore, the expression is already in simplest form.

Answer

Step: 1 ：First, we factor the numerator and denominator. The numerator factors to (2x^2 - 5x - 3 = (2x + 1)(x - 3)) and the denominator factors to (x^2 - 4 = (x - 2)(x + 2))Step: 2 ：So, our expression becomes ( frac{(2x + 1)(x - 3)}{(x - 2)(x + 2)} )Step: 3 ：We cannot simplify this any further because none of the factors in the numerator are the same as the factors in the denominator. Therefore, the expression is already in simplest form.

Simplify the rational expression \( \frac{2x^2 - 5x - 3}{x^2 - 4} \)

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