To simplify the expression, we need to find a common denominator for the two fractions. The common denominator is x(x^2 + x).

The first fraction, 1/(x+1), already has the common denominator, so we don't need to make any changes to it.

For the second fraction, x-1/(x^2+x), we need to multiply the numerator and denominator by x to get the common denominator:
(x-1)(x)/(x^2+x) * x/x = (x^2 - x)/(x^3 + x^2)

Now we can combine the fractions:
1/(x+1) - (x^2 - x)/(x^3 + x^2)

To subtract the fractions, we need to find a common denominator, which is x(x^3 + x^2).

The first fraction, 1/(x+1), needs to be multiplied by (x^2 + x)/(x^2 + x):
1/(x+1) * (x^2 + x)/(x^2 + x) = (x^2 + x)/(x^3 + x^2)

Now we can subtract the fractions:
(x^2 + x)/(x^3 + x^2) - (x^2 - x)/(x^3 + x^2)

To subtract the fractions, we can combine the numerators and keep the common denominator:
(x^2 + x - x^2 + x)/(x^3 + x^2) = (2x)/(x^3 + x^2)

Therefore, the simplified expression is 2x/(x^3 + x^2).