To simplify the algebraic expression \((x^2 + 3x - 4) / (x + 1)\), we need to factor the numerator \(x^2 + 3x - 4\) if possible, and then see if there is any common factor with the denominator \(x + 1\).
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Factor the numerator \(x^2 + 3x - 4\):
We want to find two numbers that multiply to \(-4\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers \(4\) and \(-1\) satisfy this condition since:
- \(4 \times -1 = -4\)
- \(4 + (-1) = 3\)
Thus, we can factor the quadratic expression as follows: \[ x^2 + 3x - 4 = (x + 4)(x - 1) \]
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Rewrite the expression with the factored numerator: \[ \frac{x^2 + 3x - 4}{x + 1} = \frac{(x + 4)(x - 1)}{x + 1} \]
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Check for common factors: In this case, there are no common factors between the numerator \((x + 4)(x - 1)\) and the denominator \(x + 1\).
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Final expression: Since there are no common factors to cancel, the simplified form of the expression is: \[ \frac{(x + 4)(x - 1)}{x + 1} \]
Thus, the simplified expression remains as \(\frac{(x + 4)(x - 1)}{x + 1}\). There is no further simplification possible.
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