Simplify $\tan\left(\arccos\left(\frac{x}{\sqrt{x^2+9}}\right)\right)$ as $\displaystyle
Divide fractions $\frac{\sqrt{1-\left(\frac{x}{\sqrt{x^2+9}}\right)^2}}{\frac{x}{\sqrt{x^2+9}}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$
The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
Multiplying the fraction by $-1$
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