b=(2)/(sqrt(a)+3)+(3)/(sqrt(x)-3)-frac(}{x-9)

To solve the expression \( b:\frac {2}{\sqrt {x}+3}+\frac {3}{\sqrt {x}-3}-\frac {x}{x-9} \), we need to find a common denominator and simplify the terms.<br /><br />1. **Combine the fractions:**<br /> \[<br /> \frac{2}{\sqrt{x} + 3} + \frac{3}{\sqrt{x} - 3} - \frac{x}{x - 9}<br /> \]<br /><br />2. **Find the common denominator for the first two fractions:**<br /> \[<br /> (\sqrt{x} + 3)(\sqrt{x} - 3)<br /> \]<br /><br />3. **Rewrite the first two fractions with the common denominator:**<br /> \[<br /> \frac{2(\sqrt{x} - 3)}{(\sqrt{x} + 3)(\sqrt{x} - 3)} + \frac{3(\sqrt{x} + 3)}{(\sqrt{x} + 3)(\sqrt{x} - 3)}<br /> \]<br /><br />4. **Simplify the numerators:**<br /> \[<br /> \frac{2\sqrt{x} - 6}{x - 9} + \frac{3\sqrt{x} + 9}{x - 9}<br /> \]<br /><br />5. **Combine the numerators over the common denominator:**<br /> \[<br /> \frac{(2\sqrt{x} - 6) + (3\sqrt{x} + 9)}{x - 9}<br /> \]<br /><br />6. **Simplify the combined numerator:**<br /> \[<br /> \frac{5\sqrt{x} + 3}{x - 9}<br /> \]<br /><br />7. **Subtract the third fraction:**<br /> \[<br /> \frac{5\sqrt{x} + 3}{x - 9} - \frac{x}{x - 9}<br /> \]<br /><br />8. **Combine the fractions:**<br /> \[<br /> \frac{5\sqrt{x} + 3 - x}{x - 9}<br /> \]<br /><br />9. **Rationalize the numerator:**<br /> \[<br /> \frac{5x^{\frac{3}{2}} + 3x - x^2}{x^2 - 18x + 81}<br /> \]<br /><br />10. **Simplify the numerator:**<br /> \[<br /> \frac{5x^{\frac{3}{2}} - 45\sqrt{x} - x^2 + 12x - 27}{x^2 - 18x + 81}<br /> \]<br /><br />Thus, the simplified form of the given expression is:<br />\[<br />\boxed{\frac{5x^{\frac{3}{2}} - 45\sqrt{x} - x^2 + 12x - 27}{x^2 - 18x + 81}}<br />\]