Download 7.1 Equivalent Ratonal Expressions

P20 – 7 – Rational Expressions and Equations
7.1 – Equivalent Rational Expressions
Date: _____________
7.1 Equivalent Rational Expressions
Rational Number – A number that can be written as a ratio with integer values for the numerator and denominator. A
rational number can not have zero as the denominator.
Rational Expression – an algebraic expression that can be written as the quotient of two polynomials. Rational
expressions can not contain roots of variables, or variables as exponents.
Example 1: Which of the following are rational expressions?
2𝑥+3
2𝑥 +3
𝑥 2 −6
𝑥 2 −9
5𝑥+4
4𝑥−2
3𝑥𝑦
2 √𝑥
Non-permissible Values – When rational expressions are not defined for values of the variable that make the
denominator 0.
Example 2: For which values of x is each expression defined?
12
𝑥
10 ∙ 𝑥
3+𝑥
5÷𝑥
Determining Non-Permissible Values
1) Equate the denominator to zero.
2) Solve the equation (factor).
3) Determine the non-permissible values.
Example 3: Determine the non-permissible values of each rational expression.
a)
5𝑥
𝑥 2 −9
b)
3𝑥+2
𝑥
c) 𝑥 2 +1
𝑥 2 −8𝑥+16
If you want another example of this go to page 523 example 1.
Equivalent Rational Numbers and Expressions – Numbers that have been multiplied or divided by the same
number, monomial or binomial, in the numerator and denominator. When writing equivalent expressions you must
state the non-permissible values.
Example 4: Write the following as two different equivalent rational numbers.
12
a) 18
b)
20𝑥𝑦
8𝑥 2
P20 – 7 – Rational Expressions and Equations
7.1 – Equivalent Rational Expressions
Date: _____________
Writing Equivalent Forms of a Rational Expression
1) Determine the non-permissible values.
2) Multiply or divide by a monomial or binomial in the numerator and denominator.
3) Determine the non-permissible values.
Example 5: Use multiplication or division to write two equivalent forms of the rational expression below.
(𝑥 + 5)(𝑥 − 1)
2(𝑥 − 1)
If you want another example of this go to page 524 Example 2.
Simplifying Rational Expressions
1) Factor the numerator and denominator.
2) Identify the non-permissible values.
3) Divide by common factors to simplify.
Example 6: Write each rational expression in simplest form.
−25𝑎3 𝑏2 𝑐
a)
35𝑎𝑏5
𝑥 2 −49
c) 2
𝑥 −5𝑥−14
b)
d)
6𝑥 2 +12𝑥
3𝑥
2𝑥 2 −5𝑥−3
9−𝑥 2
If you want another example of this go to page 525 example 3.