Express as a single fraction \( \frac{1}{x+1}+\frac{4}{x-2} \)

Calculate or simplify the expression \( \frac{1}{x+1}+\frac{4}{x-2} \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{x+1}+\frac{4}{x-2}\) - step1: Reduce fractions to a common denominator: \(\frac{x-2}{\left(x+1\right)\left(x-2\right)}+\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}\) - step2: Rewrite the expression: \(\frac{x-2}{\left(x+1\right)\left(x-2\right)}+\frac{4\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}\) - step3: Transform the expression: \(\frac{x-2+4\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}\) - step4: Multiply the terms: \(\frac{x-2+4x+4}{\left(x+1\right)\left(x-2\right)}\) - step5: Calculate: \(\frac{5x+2}{\left(x+1\right)\left(x-2\right)}\) - step6: Multiply the terms: \(\frac{5x+2}{x^{2}-x-2}\) The expression \( \frac{1}{x+1}+\frac{4}{x-2} \) can be simplified to \( \frac{5x+2}{x^{2}-x-2} \).