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## Homework Statement

[itex]\frac{\frac{2}{3}x(x^{2}+4)^{1/2}(x^{2}-9)^{-2/3}-x(x^{2}-9)^{1/3}(x^{2}+4)^{-1/2}}{x^{2}+4}[/itex]

## The Attempt at a Solution

[itex]\frac{x(x^{2}+4)^{-1/2}(x^{2}-9)^{-2/3}(\frac{2}{3}(x^{2}+4)-(x-9))}{x^{2}+4}[/itex]

Then:

[itex]\frac{x(\frac{2}{3}(x^{2}+4)-(x-9))}{(x^{2}+4)^{3/2}(x^{2}-9)^{2/3}}[/itex]

What should I do next? I multiply the numerator but this, it seems leads to a dead-end. Or is there a mistake involved in the aforementioned steps?

P. S. The book gives the answer

[itex]\frac{-x^{3}+35x}{3(x^{2}+4)^{3/2}(x^{2}-9)^{2/3}}[/itex]

P. S. S. Can someone tell me how to write tex instead of itex automatically?

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