(5x+3/x)-(x-1/2x)

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**Either:**

[(5x+3)/x] - [(x-1) / 2x]

adjust with common denominator, 2x:

(10x + 6)/2x - [(x-1)/2x]

distribute the negative:

10x + 6/2x + [(-x+1)/2x]

solve:

10x +6/2x + (1-x)/2x

10x + 6 +1 -x /2x

9x +7 /2x

**4.5 + 3.5x**

**--------------------------------**

*OR*

[(5x) +3/x] - [(x)-1/2x)]

distribute the negative:

5x +3/x + (-x) + 1/2x

common denominator 2x:

10x^2/2x +6/2x + (-2x^2)/2x + 1/2x

solve:

[10x^2 + 6 + (-2x^2) + 1] / 2x

(8x^2 + 7) / 2x

(8x^2 /2x ) + 7/2x

4x + 3.5x

x(4+3.5)

**7.5x**

### (5x+3/x)-(x-1/2x) :

In mathematics the first bracket is only decorative.

(5x+3/x) =5x+(3/x). And cannot mean (5x+3)/x.

-(x-1/2x) = -x+(1/2)x, and cannot mean (x-1)/(2x). 1/2x is not 1/(2x) but it means (1/2)x.

Therefore

5x+(3/x)-x+(1/2)x =5x-x+(1/2)x+(3/x)

=(5-1+0.5)x+3/x =** 4.5x+3/x**

***---*--------*-----------***

If you wanted the factors:The expression is equal to (1/x)(4.5x^2 +3) or (2/x)(9x^2 +6) .

If you wanted to solve for zeros:

No real solution and Y axis is an asymptote.

y=4.5x is another obleque asynptote.

The expression is discontinuous at x= 0 with an infinite jump from positive infinity to negative infinity as x change sign around zero i.e from ** 0+ to 0- .**

multiply top and bottom of the 1st fraction by 2 to match denominators & get

(10x + 6) /2x now rewrite the numberator to match the numerator of the second fraction so that you get

( 9x+x-1+7 ) /2x - ( x-1 )/2x )

Now write the difference of the numerators over 2x to get

( 9x+7 ) / 2x

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