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Question 48696: a+4/2 = a+4/a
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! a+4/2 = a+4/a [Find the lowest common denominator (LCD)]
(2*a) = LCD
(2a)(a+4)/2 = (2a)(a+4)/a [Multiply each fraction by the LCD]
(a)(a+4) = (2)(a+4) [Cancel wherever necessary]
a^2 + 4a = 2a + 8 [Simplify]
a^2 + 4a - 2a - 8 = 0 [Isolate all of the terms on one side of the equation]
a^2 + 2a - 8 = 0 [Combine like-terms]
(a-2)(a+4) = 0 [Factor]
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[Set each factor equal to zero and solve for "a"]
a-2=0
a=2
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or
a+4=0
a=-4
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So, a=2 or a=-4
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Check by plugging (a=2) or (a=-4) back into the original equation.
a=2
(2)+4/2 = (2)+4/(2)
6/2 = 6/2
3 = 3 [Checks out]
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a= -4
(-4)+4/2 = (-4)+4/(-4)
0/2 = 0/-4
0=0 [Checks out]
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