How do you solve \frac { x - 6} { x + 2} = \frac { x + 2} { x + 4} + 1?

1 Answer
May 4, 2018

x=-6

Explanation:

We can move everything on one side:

(x-6)/(x+2)-(x+2)/(x+4)-1=0

From there we have to find the least common multiplier, which will in this case be (x+2)(x+4):

((x+6)(x+2)(x+4))/(x+2)-((x+2)(x+2)(x+4))/(x+4)-1*(x+2)(x+4)

From there, we can cross out the mentions on the fractions:

(x+6)(x+2)-(x+2)(x+2)-(x+2)(x+4)=0

Now we can break up the parantheses_

(x-6)(x+4)=x^2-2x-24
-(x+2)(x+2)= -x^2-4x-4
-(x+2)(x+4)=-x^2-6x-8

That will give,
x^2-2x-24-x^2-4x-4-x^2-6x-8=0

Which if we shorten, is equal to_
-x^2-12x-36=0

If we now use the quadratic equation formula where a=-1, b=-12 and c=-36, we will have:

x=(-b+-sqrt(b^2-4ac))/(2a)

If we plug in the numbers here we will eventually land on:

x=-6