SOLUTION: I need help with this problem: What is the value of k if 1/(x-2)(x+4)=h/(x-2)+k/(x+4)? Answer choices: A.2, B.-4, C.-1/6, D.1/6, E.-2 What I have done so far is: multiply to cr

Question 201367: I need help with this problem:
What is the value of k if
1/(x-2)(x+4)=h/(x-2)+k/(x+4)?
Answer choices: A.2, B.-4, C.-1/6, D.1/6, E.-2
What I have done so far is: multiply to create a common denominator, which leaves me with:
1=hx+kx+4h-2k
Is this correct so far?
If so, how do I continue, and if not, what should I have done instead?
Thanks for your help.
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
1/[(x-2)(x+4)]=h/(x-2)+k/(x+4)

1=h(x+4)+k(x-2)

plug in x=-4:

1=h(0)+k(-6)

-6k=1
k=-1/6

Answer: C) -1/6
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