simplify the following rational expression. state any restrictions on the variable. m^2+4m-5 / m^2-1
To simplify the rational expression (m^2 + 4m - 5) / (m^2 - 1), we can factor both the numerator and the denominator:
Numerator: m^2 + 4m - 5 = (m + 5)(m - 1)
Denominator: m^2 - 1 = (m - 1)(m + 1)
Cancel out the common factors of (m - 1):
[(m + 5)(m - 1)] / [(m - 1)(m + 1)] = (m + 5) / (m + 1)
The simplified expression is (m + 5) / (m + 1).
Restrictions on the variable:
We must consider the restriction when the denominator is equal to zero because division by zero is undefined. In this case, m + 1 cannot equal zero, so the restriction is m ≠ -1.