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

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

╔═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╗✧   ok, now this, is epic.╚═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╝

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .