\(\displaystyle \frac{x}{x-7} - \frac{x+3}{x^2-4x-21}=\)

\(\displaystyle \frac{x}{x-7} - \frac{x+3}{(x+3)(x-7)}=\)

the factor (x+3) divides out to be 1 in the second fraction ...

\(\displaystyle \frac{x}{x-7} - \frac{1}{x-7}=\)

\(\displaystyle \frac{x-1}{x-7}\)