Simplifying the Expression: (x+1/x-1-x-1/x+1) 2x/5x-5
In this article, we will simplify the given expression: (x+1/x-1-x-1/x+1) 2x/5x-5
. To simplify this expression, we will follow the order of operations (PEMDAS) and apply the laws of algebra.
Step 1: Simplify the fraction
Let's start by simplifying the fraction (x+1/x-1-x-1/x+1)
.
(x+1/x-1-x-1/x+1) = ((x+1)/x - (x+1)/x)
Combine like terms
((x+1)/x - (x+1)/x) = (x/x + 1/x - x/x - 1/x)
= 1/x
So, the simplified fraction is 1/x
.
Step 2: Simplify the entire expression
Now, we can simplify the entire expression (1/x) 2x/5x-5
.
(1/x) 2x/5x-5 = (2x/5x) - 5/x
Cancel out the x terms
(2x/5x) = 2/5
So, the simplified expression is:
2/5 - 5/x
And that's the final answer!