Simplify (3m)/(2+ square root of m+n)

$\frac{3 m}{2 + \sqrt{m + n}}$

Multiply $\frac{3 m}{2 + \sqrt{m + n}}$ by $\frac{2 - \sqrt{m + n}}{2 - \sqrt{m + n}}$ .

$\frac{3 m}{2 + \sqrt{m + n}} \cdot \frac{2 - \sqrt{m + n}}{2 - \sqrt{m + n}}$

Multiply $\frac{3 m}{2 + \sqrt{m + n}}$ and $\frac{2 - \sqrt{m + n}}{2 - \sqrt{m + n}}$ .

$\frac{3 m (2 - \sqrt{m + n})}{(2 + \sqrt{m + n}) (2 - \sqrt{m + n})}$

Expand the denominator using the FOIL method.

$\frac{3 m (2 - \sqrt{m + n})}{4 - 2 \sqrt{m + n} + \sqrt{m + n} \cdot 2 - {\sqrt{m + n}}^{2}}$

Simplify.

$\frac{3 m (2 - \sqrt{m + n})}{- m - n + 4}$

Factor $- 1$ out of $- m$ .

$\frac{3 m (2 - \sqrt{m + n})}{- (m) - n + 4}$

Factor $- 1$ out of $- n$ .

$\frac{3 m (2 - \sqrt{m + n})}{- (m) - (n) + 4}$

Factor $- 1$ out of $- (m) - (n)$ .

$\frac{3 m (2 - \sqrt{m + n})}{- (m + n) + 4}$

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{3 m (2 - \sqrt{m + n})}{- (m + n) - 1 (- 4)}$

Factor $- 1$ out of $- (m + n) - 1 (- 4)$ .

$\frac{3 m (2 - \sqrt{m + n})}{- (m + n - 4)}$

Rewrite negatives.

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Rewrite $- (m + n - 4)$ as $- 1 (m + n - 4)$ .

$\frac{3 m (2 - \sqrt{m + n})}{- 1 (m + n - 4)}$

Move the negative in front of the fraction.

$- \frac{3 m (2 - \sqrt{m + n})}{m + n - 4}$

Simplify (3m)/(2+ square root of m+n)

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