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 first need to factor the numerator and denominator.
Numerator:
m^2 + 4m - 5 = (m + 5)(m - 1)
Denominator:
m^2 - 1 = (m + 1)(m - 1)
Now, we rewrite the expression with factored numerator and denominator:
= [(m + 5)(m - 1)] / [(m + 1)(m - 1)]
Simplify by canceling out the (m - 1) terms in the numerator and denominator:
= (m + 5) / (m + 1)
Therefore, the simplified expression is (m + 5) / (m + 1).
Restrictions on the variable:
Since the original expression contains a (m^2 - 1) in the denominator, we cannot divide by zero. Therefore, the variable m must be not equal to 1 or -1 for the expression to be valid.