PROBLEM & SOLUTION OF SIMPLIFICATION
Example.1)
A B
---------- + -----------
12 36
LCM of 12 & 36 is 36
A ( 36 ÷ 12 ) + B ( 36 ÷ 36 )
= --------------------------------
36
3A + B
= ---------------- (Ans.)
36
Example.2)
3A 5B
---------- - -----------
12 36
LCM of 12 & 36 is 36
3A ( 36 ÷ 12 ) - 5B ( 36 ÷ 36 )
= ---------------------------------------
36
3A.3 - 5B.1
= -----------------
36
9A – 5B
= -------------- = ( 9A – 5B ) / 36 (Ans.)
36
3A + 5 5B + 8A
Example.-3) Simplify ------------ + --------------
15 25
3A + 5 5B + 8A
------------ + -------------
15 25
LCM of 15 & 25 is 75
5 X (3A + 5 ) + 3 X ( 5B + 8A )
= ------------------------------------
75
15A + 25 + 15B + 24 A
= -----------------------------
75
39A + 15B + 25
= ---------------------
75
= 13A / 25 + B / 5 + 1 / 3 (Ans.)
3a ( 5b + 7c ) 5a ( 3a – 9c )
Example.-4) Simplify ---------------- + ----------------
20 30
3a ( 5b + 7c ) 5b ( 3a – 9c )
----------------- + -----------------
20 30
LCM for 20 & 30 is 60
9a ( 5b + 7c ) + 10b ( 3a – 9c )
= ---------------------------------
60
45ab + 63 ac + 30ab – 90bc
= ---------------------------------
60
= 3ab/4 + 63ac/60 + ab/2 – 3bc/2 (Ans.)
4d (a²- b²+ 9c²) 4a²(2b²+ 5c⁴-3d⁶)
Example.5) Simplify ----------------- - ------------------
36 48
4d (a²- b² + 9c²) 4a²( 2b²+ 5c⁴-3d⁶)
---------------------- - -----------------------
36 48
LCM of 36 & 48 is 144
4d (a²- b²+ 9c²) 4a²(2b²+ 5c⁴ - 3d⁶)
-------------------- - -----------------------
36 48
4 X {4d (a²- b²+ 9c²)} - 3 X {4a²( 2b² + 5c⁴- 3d⁶)}
= ---------------------------------------------------
144
16a²d – 16b²d + 144c²d - 24a²b² - 60a²c⁴ + 36a²d⁶
= ---------------------------------------------------
144
= a²d/9 - b²d/9 + c²d - a²b²/6 - 5 a²c⁴/12 + a²d⁶/4 (Ans.)