Question

What do The restrictions represent in rational expressions

Answer 1

Answer:

The real numbers that give a value of 0 in the denominator are not part of the domain. These values are called restrictions. restrictions in rational expressions make the rational expression undefined. So, the values that make the denominator zero, thus making the overall rational expression undefined represent the restrictions in rational expressions.

Step-by-step explanation:

Rational expressions usually are not defined for all real numbers. The real numbers that give a value of 0 in the denominator are not part of the domain. These values are called restrictions.

Not all rational expressions can be termed as defined for all real numbers. Certain real numbers that can make the denominator zero are not considered as part of domain. Hence, these values are said to be restrictions.

Let the rational expression be

                                                   $\frac{P}{Q}$      and Q ≠ 0

P and Q are termed as polynomials and Q can not be zero. The Q which is denominator here can not be equal to zero because we cannot divide by zero. The reason is that division by zero would make the overall rational expression undefined.

It is to be noted that numerator of rational expression can be any real number but denominator must not be zero as it would make the rational expression undefined.

Let suppose the rational expression as

                                          $\frac{3x^{2}-4 }{x-7}$

                                  ⇒ $x - 7 = 0$

                                   ⇒ $x = 7$

It is clear that the real number 7 would make the denominator zero, hence making the overall rational expression defined. So, the restricted value here be x = 7. Hence, x ≠ 0.

So, it is clear that restrictions in rational expressions make the rational expression undefined. So, the values that make the denominator zero, thus making the overall rational expression undefined represent the restrictions in rational expressions.

Keywords: rational expression, restriction values

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