Lösung 2.2:3c
Aus Online Mathematik Brückenkurs 1
Start by rewriting the terms on the left-hand side as one term having a common denominator
If we also write \displaystyle 3x-3=3(x-1), the equation can be rewritten as
Because \displaystyle x=1 cannot be a solution to the equation, the factor \displaystyle x-1 can be removed from the denominator of both sides (i.e. actually, we multiply both sides by \displaystyle x-1 and then eliminate it)
Then, both sides are multiplied by 3 and \displaystyle x+1, so that we get an equation without any denominators
Expanding both sides
The x² terms cancel each other out and we obtain a first-order equation,
which has the solution
We check whether we have calculated correctly by substituting \displaystyle x=4/5 into the original equation,
