Solution 2.2:2a

From Förberedande kurs i matematik 1

If we divide up the denominators that appear in the equation into small integer factors 6=23, 9=33 and 2, we see that the lowest common denominator is 233=18. Thus, we multiply both sides of the equation by 233 in order to avoid having denominators in the equation

23365x−2339x+2=2332135x−2(x+2)=33.

We can rewrite the left-hand side as 35x−2(x+2)=15x−2x−4=13x−4, so that we get the equation

We can now solve this first-degree equation by carrying out simple arithmetical calculations so as to get x by itself on one side:

1. Add 4 to both sides, 13x−4+4=9+4 which gives  13x=13.
2. Divide both sides by 13, 1313x=1313 which gives the answer  x=1.

The equation has x=1 as the solution.

When we have obtained an answer, it is important to go back to the original equation to check that x=1 really is the correct answer (i.e. that we haven't calculated incorrectly)

LHS=651−91+2=65−93=65−31=65−3212=65−2=63=21=RHS.