Algebra 1 Common Core Student Edition, Grade 8-9

Similarly, you can su b tract rational expressions w ith like denom inators.

Why put parentheses

around 4x + 3?

You want to subtract

the entire numerator

4x + 3, and parentheses

are needed to indicate

that. Without the

parentheses, you would

only be subtracting 4x.

W h y is t h e LCD 6 x 2
in stead o f 6x?
One of the denominators
has tw o factors o fx. So
the LCD must also have
two factors of x.

Problem 2 Subtracting Expressions W ith Like Denominators

What is the difference lx +^5 4x + 3

7x + 5

3xr - x - 2 3xz - x — 2

4x + 3 _ 7x + 5 - (4x + 3)

3x — x — 2 3x2 — x — 2 3x x — 2

7x + 5 — 4x — 3

3x2 — x - 2

3x+ 2

3x^ — x — 2

. 3 x r - r 2 ]
' 1 (3xH-~2)(x - 1 )

; 1

X — 1

G o t It? 2. W hat is th e difference?

Subtract the numerators.

Distributive Property

Simplify the numerator.

Factor the denominator. Divide out

the common factor 3x + 2.

Simplify.

z + 3 z + 3 b.

9n — 3 3n + 5

l O n — 4 l O n — 4 c.

7q — 3 6 q — 5

q 2 — 4 q 2 - 4

To ad d or subtract rational expressions w ith different denom inators, you can write the

expressions w ith th e least co m m o n d en o m in ato r (LCD).

Adding Expressions W ith Different Denominators

What is the sum6x 2x

Step 1 Find th e LCD of ^ an d First write the d en o m in ato rs 6x a n d 2x2 as

pro d u cts of prim e factors. To form th e LCD, list each factor the greatest

n u m b e r of tim es it ap p ears in a denom inator.

6x = 2 • 3 • x Factor each denominator.

2x2 = 2 • x • x

LCD = 2 • 3 • x • x = 6x2 The LCD is the LCM of 6x and 2x2.

Step 2 Rewrite each rational expression using th e LCD an d th e n add.

6x^5 + 32x2 6x Rewrite each fraction using the LCD.

2 x

5x , _9_

6x2 6x2

5x + 9

•J G o t It? 3. W hat is the

6 x

sum V

Simplify numerators and denominators.

Add the numerators.

c

Po w er A lg eb r a.co m J Lesson 11-4 Ad d ing and Su b t ract ing Rat io nal Exp ressions^685