Question

simplify the following rational expression state any restrictions on the variable
m^2+4m-5/m^2-1

Answer 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.