 Reciprocals

This part deals with reciprocals. Using the method explained below many such problems can be solved merely by mental calculation alone.

Let us consider

```
x +  1  =  10
x       3
```

Under the usual method, we cross multiply to obtain a quadratic equation which is then solved to obtain 'x'.

But by Vilokanam  sutra of Vedic mathematics, the problem can be solved merely at a glance by simple mental calculation.

```
10/3 can be written as  3 +  1/3

Therefore    x  +   1   =   3  +   1
x                3
```

==>    x  =  3   or   1/3

Similarly,

```
2)    x  +   1   =   37   =   6  +  1
x        6               6
```
```       Therefore from the sutra we have x = 6 or 1/6

3)    1    +  x + 1    =  26   =   5  +  1
x + 1      1            5                5```
```
Therefore from the sutra we have  x + 1 = 5  or  1/5
==>  x = 4   or  -4/5

4)    x - 3  +  x + 3   =   5   =  2  +  1
x + 3     x - 3        2              2```
```
Therefore  we have   x - 3   =   2  or   1
x + 3                 2
==>  x = -9 or 9

5)   x  +  1   =   13
x        6
Here 13/6 can be split up into  2/3 + 3/2

Therefore   x  +  1  =  2  +  3
x     3     2
==>   x = 2/3  or  3/2

6)     x    +  x + 1   =  25  =  3  +  4
x + 1       x          12      4     3

==>    x    =  4   or   3
x + 1      3        4

==>   x  =  -4  or  3

7)    x  -   1  =   5   =   3  -  2
x       6       2     3

Therefore  x = 3/2  or  -2/3

8)    x    -  x + 2  =  15  =  8  -  7
x + 2       x        56     7     8

==>   x    =  8  or  -7
x + 2     7        2

==>   x = -16  or  -14/9
```