Whakaoti i te 5/4-sqrt{11}-4/sqrt{11-sqrt{7}}-2/3+sqrt{7}

$$\frac { 5 } { 4 - \sqrt { 11 } } - \frac { 4 } { \sqrt { 11 } - \sqrt { 7 } } - \frac { 2 } { 3 + \sqrt { 7 } }$$

Aromātai

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Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{5}{4-\sqrt{11}} mā te whakarea i te taurunga me te tauraro ki te 4+\sqrt{11}.

$$\frac{5\left(4+\sqrt{11}\right)}{\left(4-\sqrt{11}\right)\left(4+\sqrt{11}\right)}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

Whakaarohia te \left(4-\sqrt{11}\right)\left(4+\sqrt{11}\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}.

$$\frac{5\left(4+\sqrt{11}\right)}{4^{2}-\left(\sqrt{11}\right)^{2}}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

Pūrua 4. Pūrua \sqrt{11}.

$$\frac{5\left(4+\sqrt{11}\right)}{16-11}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

Tangohia te 11 i te 16, ka 5.

$$\frac{5\left(4+\sqrt{11}\right)}{5}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

Me whakakore te 5 me te 5.

$$4+\sqrt{11}-\frac{4}{\sqrt{11}-\sqrt{7}}-\frac{2}{3+\sqrt{7}}$$

Whakangāwaritia te tauraro o \frac{4}{\sqrt{11}-\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{11}+\sqrt{7}.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)}-\frac{2}{3+\sqrt{7}}$$

Whakaarohia te \left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\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}.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{\left(\sqrt{11}\right)^{2}-\left(\sqrt{7}\right)^{2}}-\frac{2}{3+\sqrt{7}}$$

Pūrua \sqrt{11}. Pūrua \sqrt{7}.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{11-7}-\frac{2}{3+\sqrt{7}}$$

Tangohia te 7 i te 11, ka 4.

$$4+\sqrt{11}-\frac{4\left(\sqrt{11}+\sqrt{7}\right)}{4}-\frac{2}{3+\sqrt{7}}$$

Me whakakore te 4 me te 4.

$$4+\sqrt{11}-\left(\sqrt{11}+\sqrt{7}\right)-\frac{2}{3+\sqrt{7}}$$

Hei kimi i te tauaro o \sqrt{11}+\sqrt{7}, kimihia te tauaro o ia taurangi.

$$4+\sqrt{11}-\sqrt{11}-\sqrt{7}-\frac{2}{3+\sqrt{7}}$$

Pahekotia te \sqrt{11} me -\sqrt{11}, ka 0.

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

Whakangāwaritia te tauraro o \frac{2}{3+\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te 3-\sqrt{7}.

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

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}.

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

Pūrua 3. Pūrua \sqrt{7}.

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

Tangohia te 7 i te 9, ka 2.

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

Me whakakore te 2 me te 2.

$$4-\sqrt{7}-\left(3-\sqrt{7}\right)$$

Hei kimi i te tauaro o 3-\sqrt{7}, kimihia te tauaro o ia taurangi.

$$4-\sqrt{7}-3-\left(-\sqrt{7}\right)$$

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

$$4-\sqrt{7}-3+\sqrt{7}$$

Tangohia te 3 i te 4, ka 1.

$$1-\sqrt{7}+\sqrt{7}$$

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

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Tauwehe

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