Fractional equation

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In (school) algebra, a fraction equation is understood to be a determining equation with at least one fraction term that contains the unknown in the denominator .

By multiplying by the main denominator , a fraction equation can be reduced to a simpler type of equation.

example

The set of rational numbers is assumed as the basic set , i.e. H. it looks for rational numbers that satisfy this equation.

First of all, the main denominator of the three denominators must be determined, since the equation is to be multiplied by this. The denominators are therefore broken down into factors :

   | Application of the binomial formula
   | Exclude

The maximum permissible definition range of the equation can be seen in this form . It is equal to the set of rational numbers with the exception of those numbers for which at least one denominator becomes 0 when inserted into the equation. Because of the factor the number 0 is “forbidden”, because of the factor the number and because of the factor the number .

In addition, you can now see that the equation (and thus every term in the equation) with the main denominator

is to be multiplied.

Behind this multiplication infected intention of common factors in the numerators and denominators of the fracture Terme herauszukürzen , thus removing the fracture Terme.

This equation can now be further simplified by multiplying and combining similar terms:

The quadratic terms drop out when subtracted from both sides of the equation .

Subtracting the number 6 on both sides leads to:

.

Subsequent division by −6 on both sides gives the solution.

.

At this point, to be on the safe side, it must be checked whether the calculated number is an element of the definition range (see above). This is true, and the solution set is :

See also

Individual evidence

  1. a b Andreas Pfeifer: Compact course in mathematics . Oldenbourg, Munich 2007, ISBN 978-3-486-58291-8 , pp. 36 .