Transcript 3.10 Add & Subtract Rational Expressions

3.10 Warm Up
 Do
# 4, 8, & 12 on pg. 268
3.10 Add & Subtract
Rational Expressions
To +/Rational expressions must have
common denominators
 Least Common Denominator (LCD):
factor each denominator and multiply
by each factor only once
 Multiply each numerator by the LCD
 Simplify the numerator & write it
over the denominator (LCD)
 Simplify

Key to Subtracting!!!

CHANGE THE SIGN OF EVERY TERM
THAT IS SUBTRACTED!!!
EXAMPLE 1
a.
b.
Add and subtract with the same denominator
5
7
12
+
=
3x 3x 3x
Add numerators.
3 4
=3 x
Factor and divide out common factor.
= 4
x
Simplify.
3x – x + 5 3x – (x + 5)
=
x–1 x–1
x–1
=
2x – 5
x–1
Subtract numerators.
Simplify.
GUIDED PRACTICE
for Example 1
Find the sum or difference.
2
y+1
y+3
+
1. y
y = y
4x + 1 – 2x – 3 = 2x + 4
2. 2x – 1 2x – 1
2x – 1
EXAMPLE 3
Add expressions with different denominators
Find the sum 9 2 + 5 3
12x
8x
EXAMPLE 4
Subtract expressions with different denominators
Find the difference 10 – 7x .
3x
x+2
EXAMPLE 5
Subtract expressions with different denominators
Find the difference
x+4
x–1
–
.
2
2
x + 3x – 10
x + 2x – 8
x+4
x–1
–
x2 + 3x – 10
x2 + 2x – 8
=
x+4
x–1
–
(x – 2)(x + 5) (x + 4)(x – 2)
=
(x + 4)(x + 4)
(x – 1)(x + 5)
Rewrite fractions using
–
(x – 2)(x + 5) (x + 4) (x + 4)(x – 2)(x + 5) LCD, (x – 2)(x + 5)(x + 4).
= (x + 4)(x + 4) – (x – 1)(x + 5)
(x – 2)(x + 5)(x + 4)
Factor denominators.
Subtract fractions.
EXAMPLE 5
Subtract expressions with different denominators
2 + 8x + 16 – (x2 + 4x – 5)
x
=
(x – 2)(x + 5)(x + 4)
=
4x + 21
(x – 2)(x + 5)(x + 4)
Find products in
numerator.
Simplify.
GUIDED PRACTICE
for Examples 3, 4, and 5
Find the sum or difference.
3 + 14
15x
3
7
6.
=
10x 4
2x + 5x 4
7.
y2 + 5y + 3
3
y
=
+
( y +1)( y + 2)
y+2
y+1
2 – 2z – 6
z
+
1
z
2z
–
1
8. 2
–
2 – 4 = (z + 4)(z – 2)(z + 2)
z
z + 2z – 8