\(\frac{m-4}{m^2+8m+16}-\frac{m-4}{m+4}\)
We need to get a common denominator. To do that...multiply the second fraction by \( \frac{m+4}{m+4} \) .
\(=\frac{m-4}{m^2+8m+16}-\frac{(m-4)(m+4)}{(m+4)(m+4)}\)
Multiply the numerator and denominator out.
\(=\frac{m-4}{m^2+8m+16}-\frac{m^2-16}{m^2+8m+16}\)
Now that we have a common denominator, we can combine the fractions.
\(=\frac{m-4-(m^2-16)}{m^2+8m+16} \\~\\ =\frac{m-4-m^2+16}{m^2+8m+16} \\~\\ =\frac{\mathbf{-1}m^2+m+\mathbf{12}}{m^2+\mathbf{8}m+\mathbf{16}}\)
\(\frac{m-4}{m^2+8m+16}-\frac{m-4}{m+4}\)
We need to get a common denominator. To do that...multiply the second fraction by \( \frac{m+4}{m+4} \) .
\(=\frac{m-4}{m^2+8m+16}-\frac{(m-4)(m+4)}{(m+4)(m+4)}\)
Multiply the numerator and denominator out.
\(=\frac{m-4}{m^2+8m+16}-\frac{m^2-16}{m^2+8m+16}\)
Now that we have a common denominator, we can combine the fractions.
\(=\frac{m-4-(m^2-16)}{m^2+8m+16} \\~\\ =\frac{m-4-m^2+16}{m^2+8m+16} \\~\\ =\frac{\mathbf{-1}m^2+m+\mathbf{12}}{m^2+\mathbf{8}m+\mathbf{16}}\)