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Solution 2.2:2a

From Förberedande kurs i matematik 1

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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:


23365x2339x+2=2332135x2x+2=33


We can rewrite the left-hand side as 35x2x+2=15x2x4=13x4 , so that we get the equation


13x4=9


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=9+4

which gives

13x=13 .

2. Divide both sides by 13:

1313x=1313

which gives the answer x=1.

The equation has 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 = 651912=6593=6531=653212=652=63=21 = RHS