This document provides instruction on rational algebraic expressions including:
1) How to illustrate, evaluate, and find values that make rational expressions undefined.
2) Examples of evaluating expressions at given values of variables and finding values that make expressions undefined.
3) A test with problems evaluating rational expressions and finding undefined values.
2. 1. illustrate rational algebraic
expressions;
2. evaluate rational algebraic
expressions, and
3. find every value of the variables
that makes a rational expression
undefined.
3. RATIONAL ALGEBRAIC EXPRESSIONS
- A rational expression in one variable is
an expression that can be written in the
form
π·
πΈ
, where P and Q are polynomials.
π
π βπ
ππ
+ ππ β ππ
ππ + π
ππ
ππ + π
not UNDEFINED
Remember, Q β 0,
7. UNDEFINED
To make a rational expression
ππβπ
π βπ
UNDEFINED,
x β 4 = 0
equate the denominator to zero
solve for the variable x = 0 + 4
x = 4
The expression
ππβπ
π βπ
is UNDEFINED if x is replaced by
4, because the denominator would be 0.
8. UNDEFINED
To make a rational expression
ππβπ
π βπ
UNDEFINED,
x β 2 = 0
equate the denominator to zero
solve for the variable x = 0 + 2
x = 2
The expression
ππβπ
π βπ
is UNDEFINED if x is replaced by
2, because the denominator would be 0.
9. UNDEFINED
To make a rational expression
ππβπ
π βπ
UNDEFINED,
x β y = 0
equate the denominator to zero
solve for the variable x = 0 + y
x = y
The expression
ππβπ
π βπ
is UNDEFINED if the variables
x and y are replaced by equal values.
10. Test Yourself.
1. Explain how to evaluate an algebraic
expression.
2. What causes a rational expression to
be undefined?
3. How do you find the values that may
cause a rational expression to be
undefined?
11. Test Yourself.
I. Evaluate each rational expression if a = 1
and b = 2
1.
π
π2 2.
2πβπ
3ππ
II. Find the value of the variable that makes
the expression undefined.
1.
3π
4π
2.
2πβπ
πβ3