What is the simplified form of x minus 5 over x squared minus 3x minus 10 ⋅ x plus 4 over x squared plus x minus 12? (6 points)

Step 1 is to factor everything! 

After factoring you will get:

x-5 over (x+2)(x+5) times x+4 over (x-3)(x+4)

Step 2 is to remove the duplicate factors!
Remove x+4 and x+5

x-5 over (x+2)(x-5) times 1 over x-3 = 1 over x+2 times 1 over x-3 

Step 3 is to multiply the numerators and the denominators.

End result is 1 over (x+2)(x-3)