Subjects algebra

Simplify Rational 256893

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1. **State the problem:** Simplify the expression $$\frac{m^2 + m - 6}{m + 4}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor the numerator and denominator if possible, then cancel common factors. 3. **Factor the numerator:** Find two numbers that multiply to $-6$ and add to $1$ (the coefficient of $m$). $$m^2 + m - 6 = (m + 3)(m - 2)$$ 4. **Rewrite the expression:** $$\frac{(m + 3)(m - 2)}{m + 4}$$ 5. **Check for common factors:** The denominator is $m + 4$, which does not match any factor in the numerator. 6. **Conclusion:** Since there are no common factors to cancel, the simplified form is: $$\frac{(m + 3)(m - 2)}{m + 4}$$ This is the simplest form of the expression.