State any restrictions on the variables. { \frac{3y^2 - 3y}{ y - 3} }

Question:

State any restrictions on the variables. {eq}\frac{3y^2 - 3y}{ y - 3} {/eq}

Rational Expressions:

In mathematics, a rational expression is a mathematical expression in the form of a fraction, in which there is a variable in the denominator of the fraction. Because we can never divide by 0, we must always place restrictions on the variable of a rational expression. That is, the variable in a rational expression cannot be equal to a number that would create a 0 in the denominator.

Answer and Explanation:

The expression {eq}\frac{3y^{2}-3y}{y-3} {/eq} is a rational expression, because it is a fraction with a variable in the denominator. Therefore, we must place a restriction on the variable, y, that it cannot be equal to a number that would create a 0 in the denominator.

The denominator of this expression is y - 3. Therefore, we must place the restriction on y that y - 3 ≠ 0. The value of y that would make y - 3 = 0 is 3, because 3 - 3 = 0. Therefore, the restriction on y is that it cannot be equal to 3. Thus, for the expression {eq}\frac{3y^{2}-3y}{y-3} {/eq}, the variable, y, cannot be equal to 3.


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Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4
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