How do you solve #\frac { x - 5} { x } + \frac { 1} { 6} = \frac { - 1} { x }#?

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Answer 1 · 2016-10-30T17:49:40

#x=24/7#, #x!=0#

#x!=0#, since we cannot divide by 0

#(x-5)/x+1/6=-1/x#

To remove the denominator of #x#, we multiply everything by #x#.

#(x-5)/x (x)+1/6 (x)=-1/x (x)#

#x-5+x/6=-1#

#x+x/6=-1+5#

#7/6 x=4#

#7x=24#

#x=24/7#

Answer 2 · 2016-10-30T17:49:41

Please see the explanation

Add the restriction #x!=0#:

#(x - 5)/x + 1/6 = -1/x; x!=0#

We must do the above, because we are about to multiply by #6x# and multiplication by something that may be zero is invalid.

Multiply by 6x:

#6(x - 5) + x = -6; x != 0#

#6x - 30 + x = -6; x != 0#

#7x - 30 = -6; x != 0#

#7x = 24; x != 0#

#x = 24/7# and we can drop the restriction.