SIMPLIFICATION

SIMPLIFICATION :- In simplification of the numerical or mathematical expression, we follow the BODMAS rule. By using this rule in simplification, simplification becomes easy.
BODMAS stands for -

B - Brackets
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction

According to BODMAS rule, if there is a bracket we solve it first.

TYPES OF BRACKETS :- There can be more than one bracket present in a problem. If these brackets are to be given one inside the other, we use different, we use different brackets in a fixed order.

1. $\overline{\, \, \,\, \, \,}$ Bar of Vinculum
2. ( ) Round brackets or small brackets or parenthesis.
3. { } Curly brackets or Braces.
4. [ ] Square brackets or Big brackets.

If all the brackets are used in a problem, they will be placed as :
                 [ { $\overline{(\: \: \: \; \:)}$ } ]
We start solving in the same order as a given above, i.e. we start solving from inside brackets.

Some examples are given below :-
          eg.   1.     2 - [ 2 - { 2 - 2 ( 2 + 2 ) } ] = ?
               sol. =  2 - [ 2 - { 2 - 2 (4) } ]
                     =  2 - [ 2 - { 2 - 8 } ]
                     =  2 - [ 2 - { - 6 } ]
                     =  2 - [ 2 + 6 ]
                     =  2 - [ 8 ]
                     =  2 - 8
                     =  - 6

          eg.   2.     $\frac{1}{3}\, +\, \frac{1}{2}\, +\, \frac{1}{x}\, =\, 4$,  then x = ?
              
               sol.  $\Rightarrow \; \frac{1}{x}\, =\, 4\, -\, (\, \frac{1}{3}\, +\, \frac{1}{2}\, )$

                       $\Rightarrow \: \frac{1}{x}\, =\, 4\, -\, (\, \frac{2\, +\, 3}{6}\, )$

                       $\Rightarrow \: \frac{1}{x}\, =\, 4\, -\, \left ( \, \frac{5}{6} \, \right ) $

                       $\Rightarrow \: \frac{1}{x}\, =\, 4\, -\, \frac{5}{6}$

                       $\Rightarrow \: \frac{1}{x}\, =\, \frac{24\, -\, 5}{6}$

                       $\Rightarrow \: \frac{1}{x}\, =\, \frac{19}{6}$
             
               or,    $\Rightarrow \: x\, =\, \frac{6}{19}$