MCR 3U1
Lesson 4: Simplifying Rational Expressions
Unit 2
To simplify rational expressions:
 Factor the numerator and the denominator
 Cancel out common factors
To state restrictions on the variable in a rational expression, determine and exclude the value(s)
of the variable that make the denominator equal to 0 before any cancellations occur.
Example 1: Simplify and state the restrictions on the variables for each of the following.
a)
3t 3  6t 2  15t 3t (t 2  2t  5)

3t
3t
2
 t  2t  5
Restrictions:
Therefore,
b)
Restrictions:
t0
t0
c)
m2
2
m  5m  6
d)
e)
x 2  4x  4
x 2  5x  6
f)
Example 2: The ratio
is the height when the volume is
5x
x

5( x  4) x  4
x40
x  4
Therefore, x  4
y 2  10 y  25
y5
3 x
x3
represents the height of a rectangular solid. What
and the area is
? Explain how you found your answer.