Questions: (m^2-25)/(5+m)

Solution Steps

To simplify the given rational expression, we need to factor the numerator and see if there are any common factors with the denominator that can be canceled out. The numerator \(m^2 - 25\) is a difference of squares, which can be factored into \((m - 5)(m + 5)\). The denominator \(5 + m\) can be rewritten as \(m + 5\). After factoring, we can cancel the common factor in the numerator and the denominator.

The given rational expression is

\[ \frac{m^2 - 25}{5 + m} \]

The numerator \(m^2 - 25\) is a difference of squares, which can be factored as:

\[ m^2 - 25 = (m - 5)(m + 5) \]

The denominator can be rewritten as:

\[ 5 + m = m + 5 \]

Now, substituting the factored numerator and rewritten denominator into the expression, we have:

\[ \frac{(m - 5)(m + 5)}{m + 5} \]

We can cancel the common factor \(m + 5\) from the numerator and the denominator, provided \(m \neq -5\):

\[ = m - 5 \]

Final Answer