2-((x-1)/(x+2))+((2x+7)/(x^2-1x-10))

asked by guest
on Nov 25, 2024 at 8:21 pm



You asked:

Evaluate the expression: \(2 - \frac{x - 1}{x + 2} + \frac{2 x + 7}{{x}^{2} - 1 x - 10}\)

MathBot Answer:

Evaluated



\(\displaystyle 2 - \frac{x - 1}{x + 2} + \frac{2 x + 7}{{x}^{2} - 1 x - 10} = \frac{2 x + 7}{x^{2} - x - 10} - \frac{x - 1}{x + 2} + 2 \)

Expanded

\[2 - \frac{x - 1}{x + 2} + \frac{2 x + 7}{{x}^{2} - 1 x - 10} = \frac{2 x}{x^{2} - x - 10} - \frac{x}{x + 2} + 2 + \frac{7}{x^{2} - x - 10} + \frac{1}{x + 2}\]

Factored

\[2 - \frac{x - 1}{x + 2} + \frac{2 x + 7}{{x}^{2} - 1 x - 10} = \frac{x^{3} + 6 x^{2} - 4 x - 36}{\left(x + 2\right) \left(x^{2} - x - 10\right)}\]

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