Resolver 3/2sqrt{3+3}

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

Calcular

$$2\sqrt{3}-3\approx 0.464101615$$

Pasos da solución

Racionaliza o denominador de \frac{3}{2\sqrt{3}+3} mediante a multiplicación do numerador e o denominador por 2\sqrt{3}-3.

$$\frac{3\left(2\sqrt{3}-3\right)}{\left(2\sqrt{3}+3\right)\left(2\sqrt{3}-3\right)}$$

Considera \left(2\sqrt{3}+3\right)\left(2\sqrt{3}-3\right). A multiplicación pódese transformar na diferencia de cadrados mediante a regra: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{3\left(2\sqrt{3}-3\right)}{\left(2\sqrt{3}\right)^{2}-3^{2}}$$

Expande \left(2\sqrt{3}\right)^{2}.

$$\frac{3\left(2\sqrt{3}-3\right)}{2^{2}\left(\sqrt{3}\right)^{2}-3^{2}}$$

Calcula 2 á potencia de 2 e obtén 4.

$$\frac{3\left(2\sqrt{3}-3\right)}{4\left(\sqrt{3}\right)^{2}-3^{2}}$$

O cadrado de \sqrt{3} é 3.

$$\frac{3\left(2\sqrt{3}-3\right)}{4\times 3-3^{2}}$$

Multiplica 4 e 3 para obter 12.

$$\frac{3\left(2\sqrt{3}-3\right)}{12-3^{2}}$$

Calcula 3 á potencia de 2 e obtén 9.

$$\frac{3\left(2\sqrt{3}-3\right)}{12-9}$$

Resta 9 de 12 para obter 3.

$$\frac{3\left(2\sqrt{3}-3\right)}{3}$$

Anula 3 e 3.

$$2\sqrt{3}-3$$