%2F(m%2B2).jpeg "(m^2-3m-7)/(m+2)")
Simplifying the Rational Expression (m^2 - 3m - 7)/(m + 2)
This article will guide you through the process of simplifying the rational expression (m^2 - 3m - 7)/(m + 2).
Understanding Rational Expressions
A rational expression is a fraction where the numerator and denominator are both polynomials. To simplify a rational expression, we aim to factor both the numerator and denominator and cancel out any common factors.
Factoring the Numerator
The numerator, m^2 - 3m - 7, is a quadratic expression. It is not easily factorable using traditional methods, so we can't simplify it further.
Factoring the Denominator
The denominator, m + 2, is already in its simplest factored form.
Simplifying the Expression
Since the numerator cannot be factored, the entire expression is already in its simplest form:
(m^2 - 3m - 7)/(m + 2)
Important Note: Restrictions on the Variable
Remember that a fraction is undefined when the denominator is zero. Therefore, m cannot be equal to -2. We express this restriction as m ≠ -2.
Conclusion
The simplified form of the rational expression (m^2 - 3m - 7)/(m + 2) is (m^2 - 3m - 7)/(m + 2), with the restriction m ≠ -2.