\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: 3x+2+xx2+9x104x\frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \sqrt{x - 10}}{4 - x}

MathBot Answer:

Evaluated



3x+2+xx2+9x104x=xx2+3x+2+9x104x\displaystyle \frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \sqrt{x - 10}}{4 - x} = \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{3}{\sqrt{x} + 2} + \frac{9 \sqrt{x - 10}}{4 - x}


Expanded

3x+2+xx2+9x104x=xx2+3x+2+9x104x\frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \sqrt{x - 10}}{4 - x} = \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{3}{\sqrt{x} + 2} + \frac{9 \sqrt{x - 10}}{4 - x}


Factored

3x+2+xx2+9x104x=5x3220x+x29xx1010x+36x10+24(x2)(x+2)(x4)\frac{3}{\sqrt{x} + 2} + \frac{\sqrt{x}}{\sqrt{x} - 2} + \frac{9 \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)}