Download 11.4 Simplifying Rational Expressions

Algebra
11.4 Simplifying Rational Expressions
(This information will be on the STAR Test!)
Rational Expressions
Do you remember the definition of a rational number?
Any number that can be written as the quotient of two integers: ½ , 7/4 , 5 etc.
Rational Expression: a fraction whose numerator, denominator, or both
are nonzero polynomials.
2x
3
3x + 1 A rational expression is undefined when the
2
denominator is equal to zero.
x –9
x+4
x2 + 1
What values of x will make each expression undefined?
***Simplifying a fraction is actually factoring then canceling!!
16 = 8(2) = 2
40
8(5)
5
***A rational expression is simplified when the largest common factor of each
the numerator and denominator is cancelled!
Simplify
Do not cancel terms unless they are common factors of the numerator and denominator!!!
5x is not a factor of all terms, therefore you cannot cancel 5x!
1) 15 – 5x
5(3 – x)
3–x
=
=
5x
5(x)
x
A common mistake…
NOOOOO!!!!!
2)
2x2
x(2x)
2x
=
=
x2 + 5x
x(x + 5)
x+ 5
NOOOOO!!!!!
3) 5x + 3
x+ 3
=
5x + 3
x+ 3
The rational expression is already simplified!
Simplify
Let’s Try One!
1) 2x2 – 6x
=
6x2
2x(x – 3) =
2x(3x)
x–3
3x
5(3x)
=
5(1 – 2x)
3x
1 – 2x
You Try One!
2)
15x
5 – 10x
=
Recognizing Opposite Factors.
Check this out!
Simplify.
(2 – x) cannot cancel with (x – 2)
If you recognize opposites. Factor out a -1.
Watch This One!
1)
(2 – x) = -1(x – 2)
DTS
4 – x2
(2 – x)(2 + x)
=
x2 – x – 2
(x – 2)(x + 1)
-1(x – 2)(x + 2)
(x – 2)(x + 1)
=
=
x+2
x+1
Try One Together!
2) x2 + 6x + 9
(x + 3)2
=
=
9 – x2
(3 – x)(3 + x)
DTS
x+3
3–x
Try One On Your Own!
3)
5–x
5–x
=
=
x2 – 8x + 15 (x – 5)(x – 3)
-1(x – 5)
(x – 5)(x – 3)
=
1
=
x–3
1
3–x
For what values of x is the rational
expression undefined?
Basically, find the value(s) of x that make the denominator 0!
Similar to the zero-product property!
1) 15 – 5x
5x + 3
2)
3)
2x2
x2 – 16
DTS
x = -3/5
x = 4, -4
(x + 4)(x – 4)
5x + 3
x2 + 3x + 2
x = -1, -2
(x + 2)(x + 1)
One from the HW

P. 668 #30
HW

P. 667 #9-31, 42-49