Factoring usinf unlike terms

[wallee]

x/(x-7) - (x+3)/(x square -4x-21). When I factored it I got x/(x-7) -(x+3)/(x-7)(x+3). Then I got lost.

 

[wallee]

Ok so then I multiplied by the LCD which is (x-7)(x+3) then all of the X-3 canceled out and I got x/(X-7)(x-7). But the answer is x-1/x-7. I am confused

 

[skeeter]

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

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

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

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

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