add or subtract as indicate \( \frac{5 x}{x+2}+\frac{17}{x-2}-\frac{40}{x^{2}-4} \)

Calculate or simplify the expression \( \frac{5x}{x+2}+\frac{17}{x-2}-\frac{40}{x^{2}-4} \). Simplify the expression by following steps: - step0: Solution: \(\frac{5x}{x+2}+\frac{17}{x-2}-\frac{40}{x^{2}-4}\) - step1: Factor the expression: \(\frac{5x}{x+2}+\frac{17}{x-2}-\frac{40}{\left(x+2\right)\left(x-2\right)}\) - step2: Reduce fractions to a common denominator: \(\frac{5x\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{17\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{40}{\left(x+2\right)\left(x-2\right)}\) - step3: Rewrite the expression: \(\frac{5x\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{17\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{40}{\left(x+2\right)\left(x-2\right)}\) - step4: Transform the expression: \(\frac{5x\left(x-2\right)+17\left(x+2\right)-40}{\left(x+2\right)\left(x-2\right)}\) - step5: Multiply the terms: \(\frac{5x^{2}-10x+17\left(x+2\right)-40}{\left(x+2\right)\left(x-2\right)}\) - step6: Multiply the terms: \(\frac{5x^{2}-10x+17x+34-40}{\left(x+2\right)\left(x-2\right)}\) - step7: Calculate: \(\frac{5x^{2}+7x-6}{\left(x+2\right)\left(x-2\right)}\) - step8: Factor the expression: \(\frac{\left(x+2\right)\left(5x-3\right)}{\left(x+2\right)\left(x-2\right)}\) - step9: Reduce the fraction: \(\frac{5x-3}{x-2}\) The simplified expression is \( \frac{5x-3}{x-2} \).