Question 193041
1/(x-3) +1/(x+5) = (x+1)/(x-3)

multiply  both  sides  by  LCD  =(X-3)(X+5)

(x+5) +(x-3) = (x+1)(x+5)
2x+2= x^2+6x+5
subt  2x+2  both  sides
0=x^2+4x+3
factor
0=(x+1)(x+3)
set x+1=0,  x=(-1)
set x+3=0,,x=(-3)

check
(-1)  1/-4  +1/4=0/-4
-1+1=0  ok
(-3)  1/-6  +1/2=  -2/-6
-1+3=2  ok