Describe and correct the error

Question

  k   +   5   =     -2k       

k+5    k+3    k2 +8k+15
LCD= (k+3)(k+5)
k(k+3)+5(k+5)=-2k
k² +3k+5k+25=-2k
 k² +8k+25=-2k
k² +10k+25=0
       (k+5)² =0
            k=-5 

 

 

Answer 1

There are excluded values which make the denominator zero,

 which are k=-5,  and k=-3

then, solving the equation to get, k=-5, which turns out to be one of excluded values.

Therefore this rational equation has NO SOLUTION.

 

Using a graphic calculator, you can verify to see any point to meet the graph on the left side and the right side.

At k=-5, and k=-3, the two graphs have the same asymptotes but never meet.