Observe the following examples; then try to speculate on the method.
To determine the quantity that the original denominator was multiplied by to yield the new denominator, we ask, "What did I multiply the original denominator by to get the new denominator?" We find this factor by dividing the original denominator into the new denominator.
It is precisely this quantity that we multiply the numerator by to build the rational expression.
Sample set a
Determine
N in each of the following problems.
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It is important to note that we
factored
from the original denominator. We
did not multiply it by
. Had we multiplied only the denominator by
we would have had to multiply the numerator by
also.
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Practice set a
Determine
N .
The reason for building rational expressions
Building rational expressions
Normally, when we write a rational expression, we write it in reduced form. The reason for building rational expressions is to make addition and subtraction of rational expressions convenient (simpler).