Simplify:
x+2/x^2+x-2/2x Please Show All Work!
Simplify 2+4-5
To simplify the expression (x + 2) / (x^2 + x) - (2x - 2) / 2x, we'll first find a common denominator for the two fractions. The common denominator is 2x.
Now, let's simplify each fraction individually:
For the first fraction (x + 2) / (x^2 + x):
To simplify this fraction, we can factor the denominator.
x^2 + x can be factored as x(x + 1).
So, the first fraction becomes (x + 2) / x(x + 1).
For the second fraction (2x - 2) / 2x:
We can factor out a 2 from the numerator.
The second fraction becomes 2(x - 1) / 2x.
The 2's cancel out and the fraction simplifies to (x - 1) / x.
Now, let's rewrite the original expression with the common denominator:
(x + 2) / x(x + 1) - (2(x - 1)) / 2x
Next, we combine the fractions by subtracting them. To subtract fractions, they must have the same denominator.
[((x + 2) - 2(x - 1)) / x(x + 1)] / 2x
Now, we expand and simplify the numerator:
[x + 2 - 2x + 2] / x(x + 1)
Simplifying further, we get:
[-x + 4] / x(x + 1)
So, the simplified expression is (-x + 4) / (x(x + 1)).