Question #939a5

2 Answers
Azimet
Feb 11, 2017

#x = 4#

Explanation:

We need to remember that #a/b = c/d => ad = bc#

We can rewrite the equation as: #2(2x+4) = 12(x-2)#

#=> 4x + 8 = 12x - 24 => 8x = 32 => x = 4#

Normally, we would also take the restrictions #x != +-2# to make sure no denominator was zero, but this solution is fine.

Alan P.
Feb 11, 2017

#x=4#

Explanation:

Given: #color(red)(12/(2x+4))=color(blue)(2/(x-2))#
Note that the given expression is meaningless unless #x!=-2# and #x!=2#
... so we will make the assumption that these conditions have been met.

#color(red)(12/(2x+4)) * (x-2)/(x-2) = color(blue)(2/(x-2)) * (2x+4)/(2x+4)#

#color(green)((12x-24))/color(magenta)((2x+4) * (x-2)) = color(brown)((4x +8))/color(magenta)((2x+4) * (x-2))#

#color(green)(12x-24)=color(brown)(4x+8)#

#8x=32#

#x=4#

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