# Solve #1/x + 1/(x+4) = 1/3# ?

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These are all fractions and I know I have to create a common denominator.

These are all fractions and I know I have to create a common denominator.

##### 1 Answer

Nov 17, 2017

#### Explanation:

Given:

#1/x+1/(x+4)=1/3#

Multiply both sides of the equation by

#3(x+4)+3x=x(x+4)#

which multiplies out to:

#3x+12+3x=x^2+4x#

That is:

#6x+12 = x^2+4x#

Subtract

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

#color(white)(0) = x^2-2x+1-13#

#color(white)(0) = (x-1)^2-(sqrt(13))^2#

#color(white)(0) = ((x-1)-sqrt(13))((x-1)+sqrt(13))#

#color(white)(0) = (x-1-sqrt(13))(x-1+sqrt(13))#

So:

#x = 1+-sqrt(13)#

These are both solutions of the original equation since they do not cause any of the denominators to becomes zero.