(x^(2)-2)/(x^(2)-4)+(x^(2))/(x-2)-(x^(3)+x-4)/(x^(2)-4)

asked by guest
on Jan 26, 2025 at 11:30 am



You asked:

Evaluate the expression: \(\frac{{x}^{2} - 2}{{x}^{2} - 4} + \frac{{x}^{2}}{x - 2} - \frac{{x}^{3} + x - 4}{{x}^{2} - 4}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{{x}^{2} - 2}{{x}^{2} - 4} + \frac{{x}^{2}}{x - 2} - \frac{{x}^{3} + x - 4}{{x}^{2} - 4} = \frac{x^{2}}{x - 2} + \frac{x^{2} - 2}{x^{2} - 4} - \frac{x^{3} + x - 4}{x^{2} - 4} \)

Expanded

\[\frac{{x}^{2} - 2}{{x}^{2} - 4} + \frac{{x}^{2}}{x - 2} - \frac{{x}^{3} + x - 4}{{x}^{2} - 4} = - \frac{x^{3}}{x^{2} - 4} + \frac{x^{2}}{x - 2} + \frac{x^{2}}{x^{2} - 4} - \frac{x}{x^{2} - 4} + \frac{2}{x^{2} - 4}\]

Factored

\[\frac{{x}^{2} - 2}{{x}^{2} - 4} + \frac{{x}^{2}}{x - 2} - \frac{{x}^{3} + x - 4}{{x}^{2} - 4} = \frac{3 x^{2} - x + 2}{\left(x - 2\right) \left(x + 2\right)}\]

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