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A rational expression is undefined when the denominator is equal to zero. To find the values that make a rational expression undefined, set the denominator ...
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Math 51 Worksheet
A rational expression is an expression of the form , Q
p
where P and Q are polynomials, with Q โ 0.
Example: (^42)
3 5 8
x x
x x โ
โ (^) Is a rational expression because the top and bottom are polynomials.
Example: x x
x x 5 8
4
8 โ
โ โ โ Is not because of the negative power and the square root.
What makes a rational expression undefined?
A rational expression is undefined when the denominator is equal to zero. To find the values that make a rational expression undefined, set the denominator equal to zero and solve the resulting equation.
Example: 0
2 x^3 โ 7 x Is undefined because the zero is in the denominator.
Write the rational expression in lowest terms: 6 15
x
x x
o Factor the numerator 6 15
x
x x
o Factor the denominator 3 ( 2 5 )
x
x x
o Divide out common factors 3
โ +^ โ x x x
x x
Find any values of the variable for which each rational expression is undefined.
x
x x 2) 9
m
m
2
2
r r
r (^) 4) 5 10
2
2
w
w w
Write each rational expression in lowest terms.
7 3
x
x (^) 6) 4 8
x
x
2
3 2
x x
x x x use grouping 8) 8 12
2
2
x x
x x
p
p (^) use difference of cubes 10) 5 2
x
x
Answer Key
x โ โ 4 2) m โ 3 m โ โ 3
2 2
r โ โ^5 r โ 4)^ It is never undefined
5 ) 7 x^5 6) 2
x
x (^) 8) 2
x
x