Adding & Subtracting Rational Expressions - Metropolitan Community College

ADDING AND SUBTRACTING RATIONAL EXPRESSIONS

To Add or Subtract Two Fractions

H J H)J

) /

, IK0

I

I

I

Example 1

&

a) Add

'(

&

Solution: a)

'(

*

)

)

H J H-J

- /

, IK0

I

I

I

b) Subtract

'(

*

'(

/

&0*

'(

/

'+

b)

'(

+

,

-

'

,

/

+

-

'

+1'

/

,

,

,

2

,

The same principles apply when adding or subtracting rational expressions containing

variables.

To Add or Subtract Rational Expressions with a Common Denominator

1. Add or subtract the numerators.

2. Place the sum or difference of the numerators found in step 1 over

the common denominator.

3. Simplify the faction if possible.

Example 2

Add

Solution:

Example 3

Add

Solution:

(

;1+

(

;1+

;0<

) ;1+

)

;0<

;1+

; > 0?;1<

=;0+)=;1 0?;1<

=;0+)=;1 1 2;1+

; > 0&;0'<

Solution:

; > 1 0&;0'<

-

; > 1 2;1+

; > 0&;0'<

/

=; > 1 1 2;1+)

; > 0&;0'<

/

; > 1 02;0+

; > 0&;0'<

0&;0'<

/

28Q < X ? . To do this, we multiply the fraction on the left by &R > and the fraction on the

right by

+

2; > R

)

(;

R V

/

?+R > 0 (;

R V

or

(; 0 ?+R >

R V

and the second fraction by

1 ?;1 ................
................

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