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Describe and correct the error


  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 
 
 
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1 Answer

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.