# 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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