SOLUTION: Solve the equation. {{{(k)/(7-k)-(2)/(k)=3}}}

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Question 46979: Solve the equation.
%28k%29%2F%287-k%29-%282%29%2F%28k%29=3
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
%28k%29%2F%287-k%29-%282%29%2F%28k%29=3[Find the lowest common denominator (LCD) = (7-k)(k)]
%28k%29%287-k%29%28k%29%2F%287-k%29-%282%29%287-k%29%28k%29%2F%28k%29=3%287-k%29%28k%29%29[Multiply terms by the LCD]
%28%28k%29%28k%29%29-%28%282%29%287-k%29%29=3%287-k%29%28k%29%29%29 [Cancel out]
%28%28k%5E2%29%29-%28%2814-2k%29%29=%28%2821k-3k%5E2%29%29%29%29[Multiply]
%28%28k%5E2%29%29-%28%2814-2k%29%29=%28%2821k-3k%5E2%29%29%29%29[Subtract the left side]
%28%28k%5E2%2B3k%5E2%29-14%2B2k-21k%29
%28%284k%5E2-14-19k%29%29%29%29 [Combine like-terms]
%28%284k%5E2-19k-14%29%29%29%29 [Rearrange the terms]
.
x=%28--19+%2B-+sqrt%28+%28-19%5E2%29-%284%29%284%29%28-14%29+%29%29%2F%28%282%29%284%29%29 [Plug into the quadratic formula]
x=%2819+%2B-+sqrt%28+%28585%29+%29%29%2F%28%288%29%29 [Plug into the quadratic formula]
x=%2819+%2B-+sqrt%28+%289%29%2865%29+%29%29%2F%28%288%29%29
x=%2819+%2B-+3sqrt%28%2865%29+%29%29%2F%28%288%29%29
x=5.398
x=-0.6483