e) \( \frac{2}{x^{2}+3 x+2}-\frac{1}{x^{2}+x-2}-\frac{1}{x^{2}-1} \)

Calculate or simplify the expression \( 2/(x^2+3*x+2)-1/(x^2+x-2)-1/(x^2-1) \). Simplify the expression by following steps: - step0: Solution: \(\frac{2}{\left(x^{2}+3x+2\right)}-\frac{1}{\left(x^{2}+x-2\right)}-\frac{1}{\left(x^{2}-1\right)}\) - step1: Remove the parentheses: \(\frac{2}{x^{2}+3x+2}-\frac{1}{x^{2}+x-2}-\frac{1}{x^{2}-1}\) - step2: Factor the expression: \(\frac{2}{\left(x+1\right)\left(x+2\right)}-\frac{1}{\left(x-1\right)\left(x+2\right)}-\frac{1}{\left(x+1\right)\left(x-1\right)}\) - step3: Reduce fractions to a common denominator: \(\frac{2\left(x-1\right)}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}-\frac{x+1}{\left(x-1\right)\left(x+2\right)\left(x+1\right)}-\frac{x+2}{\left(x+1\right)\left(x-1\right)\left(x+2\right)}\) - step4: Rewrite the expression: \(\frac{2\left(x-1\right)}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}-\frac{x+1}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}-\frac{x+2}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}\) - step5: Transform the expression: \(\frac{2\left(x-1\right)-\left(x+1\right)-\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}\) - step6: Multiply the terms: \(\frac{2x-2-\left(x+1\right)-\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}\) - step7: Subtract the terms: \(\frac{-5}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}\) - step8: Rewrite the fraction: \(-\frac{5}{\left(x+1\right)\left(x+2\right)\left(x-1\right)}\) - step9: Calculate: \(-\frac{5}{x^{3}+2x^{2}-x-2}\) The simplified expression is \( -\frac{5}{x^{3}+2x^{2}-x-2} \).