How do you solve #1/(2x) + 3/(x+7) = -1/x# and find any extraneous solutions?

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Answer 1 · 2016-07-17T05:23:02

#x=-7/3#

First, you can write the equivalent equation:

#1/(2x)+3/(x+7)+1/x=0#

and then have a single fraction, by multiplying all terms by 2x(x+7),

if #x!=0 and x!=-7#:

#1/cancel(2x)cancel(2x) (x+7)+3/cancel(x+7)2x(cancel(x+7))+1/cancelx2cancelx(x+7)=0#

#x+7+6x+2x+14=0#

#9x+21=0#

#x=-21/9=-7/3#