\frac{3}{\sqrt{x}+2}+\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{9\sqrt{x-10}}{4-x}

asked by guest
on Nov 20, 2024 at 5:37 am



You asked:

Evaluate the expression: \(\frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \cdot \sqrt{x - 10}}{4 - x}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \cdot \sqrt{x - 10}}{4 - x} = \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{3}{\sqrt{x} + 2} + \frac{9 \sqrt{x - 10}}{4 - x} \)

Expanded

\[\frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \cdot \sqrt{x - 10}}{4 - x} = \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{3}{\sqrt{x} + 2} + \frac{9 \sqrt{x - 10}}{4 - x}\]

Factored

\[\frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \cdot \sqrt{x - 10}}{4 - x} = \frac{5 x^{\frac{3}{2}} - 20 \sqrt{x} + x^{2} - 9 x \sqrt{x - 10} - 10 x + 36 \sqrt{x - 10} + 24}{\left(\sqrt{x} - 2\right) \left(\sqrt{x} + 2\right) \left(x - 4\right)}\]

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