Rational Algebraic Expressions
Rational Algebraic Expressions
4. Rational Algebraic Expressions
Note You need to understand how to multiply algebraic expressions using the distributive law before starting work on this tutorial. If you feel you need to review this, go back to 3. Multiplying and Factoring Algebraic Expressions.
Q What is a Rational Expression?
Rational Expression
A rational expression is an algebraic expression of the form P/Q, where P and Q are simpler expressions (usually polynomials), and the denominator Q is not zero.
A rational number is any number that can be written in the form a/b, where a and b are integers and b ≠ 0. it is necessary to exclude 0 because the fraction represents a ÷ b, and division by zero is undefined.
A rational expression is an expression that can be written in the form P/Q where P and Q are polynomials and the value of Q is not zero.
Some examples of rational expressions:
-5/3; (x^2 + 1)/2; 7/(y -1); (ab)/c; [(a^2)(b]/c^2; (z^2 + 3z + 2)/ (z + 1) ect.
Like a rational number, a rational expression represents a division, and so the denominator cannot be 0. A rational expression is undefined for any value of the variable that makes the denominator equal to 0. So we say that the domain for a rational expression is all real numbers except those that make the denominator equal to 0.
Examples:
1) x/2
Since the denominator is 2, which is a constant, the expression is defined for all real number values of x.
2) 2/x
Since the denominator x is a variable, the expression is undefined when x = 0
3) 2/(x - 1) x - 1 ≠ 0 x ≠ 1
The domain is {x| x ≠ 1}. Or you can say:
The expression is undefined when x = 1.
4) 2/(x^2 + 1)
Since the denominator never will equal to 0, the domain is all real number values of x.
Algebra of Rational Expression Rule | Example | Multiplication: | P
Q | | R
S | = | PR
QS | | | x + 1
x | | (x - 1)
2x + 1 | = | (x - 1)(x + 1)
x(2x + 1) | = | x2 - 1
4. Rational Algebraic Expressions
Note You need to understand how to multiply algebraic expressions using the distributive law before starting work on this tutorial. If you feel you need to review this, go back to 3. Multiplying and Factoring Algebraic Expressions.
Q What is a Rational Expression?
Rational Expression
A rational expression is an algebraic expression of the form P/Q, where P and Q are simpler expressions (usually polynomials), and the denominator Q is not zero.
A rational number is any number that can be written in the form a/b, where a and b are integers and b ≠ 0. it is necessary to exclude 0 because the fraction represents a ÷ b, and division by zero is undefined.
A rational expression is an expression that can be written in the form P/Q where P and Q are polynomials and the value of Q is not zero.
Some examples of rational expressions:
-5/3; (x^2 + 1)/2; 7/(y -1); (ab)/c; [(a^2)(b]/c^2; (z^2 + 3z + 2)/ (z + 1) ect.
Like a rational number, a rational expression represents a division, and so the denominator cannot be 0. A rational expression is undefined for any value of the variable that makes the denominator equal to 0. So we say that the domain for a rational expression is all real numbers except those that make the denominator equal to 0.
Examples:
1) x/2
Since the denominator is 2, which is a constant, the expression is defined for all real number values of x.
2) 2/x
Since the denominator x is a variable, the expression is undefined when x = 0
3) 2/(x - 1) x - 1 ≠ 0 x ≠ 1
The domain is {x| x ≠ 1}. Or you can say:
The expression is undefined when x = 1.
4) 2/(x^2 + 1)
Since the denominator never will equal to 0, the domain is all real number values of x.
Algebra of Rational Expression Rule | Example | Multiplication: | P
Q | | R
S | = | PR
QS | | | x + 1
x | | (x - 1)
2x + 1 | = | (x - 1)(x + 1)
x(2x + 1) | = | x2 - 1