Will J.

asked • 05/25/14

why do you need to find restrictions when solving rationals ?

I dont understand

Philip P.

tutor
Rational expressions are fractions and the denominator is not allowed to equal zero, since division by zero is undefined.  For example:
 
(x2-4)/x(x+4)
 
The denominator = 0 when x=0 or when x=-4, so those points are not part of the domain of the expression.  You can simplify the above expression as follows:
 
(x2-4)/x(x+4) = (x+4)(x-4)/x(x+4) = (x-4)/x
 
However, this simplified expression is valid only where x≠0 and x≠-4 since the original expression is undefined at those points.  Hence, x≠0 and x≠-4 are the restrictions that apply to the simplification.
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05/25/14

Philip P.

tutor
Sorry, numerator in my example should be x2-16 ...
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05/25/14

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Dorene O. answered • 05/28/14

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There are two major restrictions when solving radicals, such as sqrt(x) or 1/(sqrt(x). The first is that we can not take the square root of a negative number using R, that is, real numbers. If x is less than 0, the root is undefined unless we use i, the imaginary root which when squared = -1.
 
The second major restriction is that division by zero is undefined. So if the expression in the denominator turns out to be 0, that is undefined. In the above example, 1/sqrt(x) has a restriction where x < or = zero.
 
Dorene O.
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