Question

What is the sum? 1/x+2+1/x+3+1/x^2+5x+6

Answer 1

Kids these days, dont know how to add fractions..
(1/x) + (2/1)`+ (1/x) + (3/1) + (1/x^2) + (5x/1) + (6/1)
Notice every number like..2, 3 and 6 I put over 1, becuase it does not change its value..3/1 = 3 for example[m any number divided by 1 = the same number].
but I did this, so I could express all the terms in the question as fractions.

Now, to add fraction we have to find a common denominator. but all our denominators (the number at the bottom of the fraction.i.e. below the line) are different. 

However, x^2 being the highest power seems to solve this. so , here are the steps to solve this:
1. look at the first term (1/x), the denominator [the number below the line] is x. Now if we divide that into our common denominator, the result is x. Let me show you:

x ^2/x = x [ because x multiplied by x  or x squared is equal to x^2]

Now since we know, that x into x^2 is x we multiply that by the numerator [the number on top of the line] which in this case is 1, so so far we have:

x
---
x^2   

next : we have the term  (2/1). Well, the denominator 1 divides into the common denominator x^2 times, so the result is now: 

x + 2(x^2) +
--------------
   x^2

and on and on...till we get to ..

x + 2x^2 + x + 3x ^2 + 1 + 5x ^3 + 6x ^2
---------------------------------------------------------
                 x^2

   b