## How do you evaluate an expression example?

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

## Which expression is equivalent to 7xy?

Answer Expert Verified 7(xy) = (7x)y = 7xy .

## What is the definition of equivalent expressions?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

## How do you know if rational expressions are equivalent?

Multiplying top and bottom of a rational expression by the same number will result in an equivalent rational expression. The same is true if we multiply top and bottom by some polynomials.

## What is the definition of a rational expression?

A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.

## Which of the following is the best definition for a rational expression?

The ratio of two polynomials. It is “Rational” because one is divided by the other, like a ratio. Note: the polynomial we divide by cannot be zero.

## How do you describe a rational function?

A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1 . In other words, there must be a variable in the denominator. The general form of a rational function is p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .

## What does the word restrictions mean in connection with a rational expression?

Restrictions are limitations set on the value of a variable. In a rational expression, — is undefined, so the. variable can not equal a value that results in the denominator being equal to 0. Restrictions must be stated. to avoid undefined values.

## How important is simplifying of rational expressions?

Simplifying rational expressions will make the further calculations easier since the variables to work with will usually be smaller. To determine that a rational expression is in simplest form we need to make sure that the numerator and the denominator have no common variables.

## Can a rational expression have no restrictions?

If the variable is a real number, then a rational function such as 1/(x 2+1) has no domain restrictions, since the deniminator can never be zero. If the variable is a complex number, then there will always be a restriction, since every polynomial has roots in the field of complex numbers. Thank you! Yes.

## Why is the domain important for rational expressions?

When simplifying rational expressions, it is a good habit to always consider the domain, and to find the values of the variable (or variables) that make the expression undefined. (This will come in handy when you begin solving for variables a bit later on.)