b) (x+1)/(x^3)cdot (x^2-x+1-(x^3)/(x+1))

1. **Find a common denominator for the terms inside the parentheses:** The common denominator is (x+1).<br /><br />2. **Rewrite the expression inside the parentheses with the common denominator:** $x^2 - x + 1 - \frac{x^3}{x+1} = \frac{(x^2-x+1)(x+1) - x^3}{x+1}$<br /><br />3. **Expand the numerator:** $(x^2-x+1)(x+1) - x^3 = x^3 + x^2 - x^2 - x + x + 1 - x^3 = 1$<br /><br />4. **Substitute back into the original expression:** $\frac{x+1}{x^3} \cdot \frac{1}{x+1}$<br /><br />5. **Simplify:** $\frac{1}{x^3}$<br />