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Algebraic Fractions

(1) To simplify algebraic fractions, find the lowest common multiple (LCM) of the denominators and multiply the numerators by the quotient of the LCM over their respective denominators. (2) This allows combining like terms in the numerators over a common denominator. (3) Examples are provided to demonstrate simplifying fractions with algebraic expressions in the numerators and denominators.

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163 views3 pages

Algebraic Fractions

(1) To simplify algebraic fractions, find the lowest common multiple (LCM) of the denominators and multiply the numerators by the quotient of the LCM over their respective denominators. (2) This allows combining like terms in the numerators over a common denominator. (3) Examples are provided to demonstrate simplifying fractions with algebraic expressions in the numerators and denominators.

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© © All Rights Reserved
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ALGEBRAIC FRACTIONS

When simplifying algebraic fractions we follow the same


procedure as in arithmetic.
(1) Find LCM of each term in denominators.
(2) Multiply each numerator by the result we get
when the LCM is divided by the denominator
corresponding to the numerator.
(3) Then simplify numerator.

EXAMPLE: EXAMPLE:

2 a - 3 5a + 2
Simplify -
4 6

SOLUTION

2 a - 3 5a + 2
-
4 6
( i ) Find the LCM of 4 and 6 = 12
LCM
( ii ) gives 3, multiply 2a - 3 by 3
4
LCM
( iii ) gives 2, multiply 5a + 2 by 2
6
EXAMPLE: Using the distributive law,
Simplify
7
+
5 3 ( 2 a - 3 ) - 2 ( 5a + 2 )
9 pq 18 p ,
12
SOLUTION we get,
The LCM of 9 pq and 18p is 18pq 6a - 9 - 10a - 4
,
7 5 12
Thus +
9 pq 18 p group like terms then simplify
2 ( 7 ) + q ( 5) 6a - 10a - 9 - 4 -4a - 13
=
18 pq 12 12
14 + 5q

18 pq

EXAMPLE: EXAMPLE:
3 5
Simplify + expressing
Express as a single fraction x-2 x+3
5 p your answer as a single fraction.
-
q 3
SOLUTION
SOLUTION
EXAMPLE:

Express as a single fraction


2m 5m
-
n 3n

SOLUTION

The LCM of n and 3n is 3n


2m 5m
Thus -
n 3n
3 ( 2 m ) - 1 ( 5m )

3n
6m - 5m

3n
m

3n

EXERCISE C7

Express the following as single fractions:

3p q a 3a
+ +
(1) 2 p (2) 5 2
x - 2 x+1 x- 3 x- 2
+ -
(3) 3 4 (4) 3 5

5p +2 3p -1 2k 2 -k
- +
(5) 3 4 (6) 3 5

3 4
+
(7) x x+1 (8)
3 5
+
x - 2 x+3

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