How do you solve #\frac{2}{x}=\frac{x-4}{6}#?

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Answer 1 · 2017-06-24T05:15:46

#x# = #6# or #-2#

You multiply both sides of the equation by the LCM, which is #6x#.

#2/x * 6x # = #(x-4)/6 * 6x#

The #x# on the left side cancels out, while the #6# on the right side cancels out.

#2*6# = #x(x-4)#

Now, you have to expand both sides and if possible, simplify.

#12# = #x^2-4x#

Bring everything to one side.

#x^2 - 4x- 12 =0 #

Now, factor. The numbers you can use are #2# and #-6#, since they are multiples of #-12#, and when combined, they give the number #-4#.

#(x+2)(x-6)=0#

Now, you have to solve for zero within the parentheses to get the final answers.

#x+2=0#

Therefore,

#x=-2#

Also,

#x-6=0#

Therefore,

#x=6#

So, your final answer is that #x=-2, or x=6#

Happy Solving!