limits. with fractions in the numerator

Question

lim x→0 

 

(1/4)-(1/(x+4))

        x

 

Step 1 would be to get common denominators on the top so....

       (1/4)  - (1/(x+4))   =     1   -  1      = 1 (x+4)    -  1(4)
         x            x                   4     x+4       4(x+4)        (4)x+4

which is where i got stuck i got

(x+4)-4  

4(x+4)

-Which then would cancel top and bottom to where its 

(x+4)-4 = -4=   -1
4(x+4)       4    

 

but i dont think thats correct please correct me and tell me where i got wrong

 

 

 

Answer 1

No reason to do common denominators.  Plug in the 0 and you have 1/4-1/4=0