Whakaoti i te 9/sqrt{7-2}-4/3+sqrt{7}+5/sqrt{6-sqrt{7}}

$$\frac { 9 } { \sqrt { 7 } - 2 } - \frac { 4 } { 3 + \sqrt { 7 } } + \frac { 5 } { \sqrt { 6 } - \sqrt { 7 } }$$

Aromātai

$$-5\sqrt{6}\approx -12.247448714$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{9}{\sqrt{7}-2} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}+2.

$$\frac{9\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Whakaarohia te \left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{9\left(\sqrt{7}+2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Pūrua \sqrt{7}. Pūrua 2.

$$\frac{9\left(\sqrt{7}+2\right)}{7-4}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Tangohia te 4 i te 7, ka 3.

$$\frac{9\left(\sqrt{7}+2\right)}{3}-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Whakawehea te 9\left(\sqrt{7}+2\right) ki te 3, kia riro ko 3\left(\sqrt{7}+2\right).

$$3\left(\sqrt{7}+2\right)-\frac{4}{3+\sqrt{7}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Whakangāwaritia te tauraro o \frac{4}{3+\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 3-\sqrt{7}.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Whakaarohia te \left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Pūrua 3. Pūrua \sqrt{7}.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{9-7}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Tangohia te 7 i te 9, ka 2.

$$3\left(\sqrt{7}+2\right)-\frac{4\left(3-\sqrt{7}\right)}{2}+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Whakawehea te 4\left(3-\sqrt{7}\right) ki te 2, kia riro ko 2\left(3-\sqrt{7}\right).

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5}{\sqrt{6}-\sqrt{7}}$$

Whakangāwaritia te tauraro o \frac{5}{\sqrt{6}-\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}+\sqrt{7}.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{\left(\sqrt{6}-\sqrt{7}\right)\left(\sqrt{6}+\sqrt{7}\right)}$$

Whakaarohia te \left(\sqrt{6}-\sqrt{7}\right)\left(\sqrt{6}+\sqrt{7}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$

Pūrua \sqrt{6}. Pūrua \sqrt{7}.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{6-7}$$

Tangohia te 7 i te 6, ka -1.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)+\frac{5\left(\sqrt{6}+\sqrt{7}\right)}{-1}$$

Ko te mea whakawehea ki te -1 ka hōmai i tōna kōaro.

$$3\left(\sqrt{7}+2\right)-2\left(3-\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te \sqrt{7}+2.

$$3\sqrt{7}+6-2\left(3-\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 3-\sqrt{7}.

$$3\sqrt{7}+6-\left(6-2\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

Hei kimi i te tauaro o 6-2\sqrt{7}, kimihia te tauaro o ia taurangi.

$$3\sqrt{7}+6-6-\left(-2\sqrt{7}\right)-5\left(\sqrt{6}+\sqrt{7}\right)$$

Ko te tauaro o -2\sqrt{7} ko 2\sqrt{7}.

$$3\sqrt{7}+6-6+2\sqrt{7}-5\left(\sqrt{6}+\sqrt{7}\right)$$

Tangohia te 6 i te 6, ka 0.

$$3\sqrt{7}+2\sqrt{7}-5\left(\sqrt{6}+\sqrt{7}\right)$$

Pahekotia te 3\sqrt{7} me 2\sqrt{7}, ka 5\sqrt{7}.

$$5\sqrt{7}-5\left(\sqrt{6}+\sqrt{7}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -5 ki te \sqrt{6}+\sqrt{7}.

$$5\sqrt{7}-5\sqrt{6}-5\sqrt{7}$$

Pahekotia te 5\sqrt{7} me -5\sqrt{7}, ka 0.

$$-5\sqrt{6}$$