Resolver frac{sqrt{5}}{12}-frac{3sqrt{6}}{8}+frac{2sqrt{5}}{3}+frac{sqrt{6}}{4}-frac{3sqrt{5}}{4}-frac{sqrt{6}}{2}

$$\frac { \sqrt { 5 } } { 12 } - \frac { 3 \sqrt { 6 } } { 8 } + \frac { 2 \sqrt { 5 } } { 3 } + \frac { \sqrt { 6 } } { 4 } - \frac { 3 \sqrt { 5 } } { 4 } - \frac { \sqrt { 6 } } { 2 }$$

Avaliar

$$-\frac{5\sqrt{6}}{8}\approx -1,530931089$$

Passos Para a Resolução

Combine \frac{\sqrt{5}}{12} e \frac{2\sqrt{5}}{3} para obter \frac{3}{4}\sqrt{5}.

$$\frac{3}{4}\sqrt{5}-\frac{3\sqrt{6}}{8}+\frac{\sqrt{6}}{4}-\frac{3\sqrt{5}}{4}-\frac{\sqrt{6}}{2}$$

Combine -\frac{3\sqrt{6}}{8} e \frac{\sqrt{6}}{4} para obter -\frac{1}{8}\sqrt{6}.

$$\frac{3}{4}\sqrt{5}-\frac{1}{8}\sqrt{6}-\frac{3\sqrt{5}}{4}-\frac{\sqrt{6}}{2}$$

Combine \frac{3}{4}\sqrt{5} e -\frac{3\sqrt{5}}{4} para obter 0.

$$-\frac{1}{8}\sqrt{6}-\frac{\sqrt{6}}{2}$$

Combine -\frac{1}{8}\sqrt{6} e -\frac{\sqrt{6}}{2} para obter -\frac{5}{8}\sqrt{6}.

$$-\frac{5}{8}\sqrt{6}$$