How do you solve x−6x+2=x+2x+4+1?

1 Answer
Daniel
May 4, 2018

x=−6

Explanation:

We can move everything on one side:

x−6x+2−x+2x+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)=x2−2x−24
−(x+2)(x+2)=−x2−4x−4
−(x+2)(x+4)=−x2−6x−8

That will give,
x2−2x−24−x2−4x−4−x2−6x−8=0

Which if we shorten, is equal to_
−x2−12x−36=0

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

x=−b±√b2−4ac2a

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

x=−6

Related questions
Impact of this question
1202 views around the world
You can reuse this answer
Creative Commons License