Whakaoti i te frac{7+sqrt{6}}{7-sqrt{6}}-frac{7-sqrt{6}}{7+sqrt{6}}

$$\frac { 7 + \sqrt { 6 } } { 7 - \sqrt { 6 } } - \frac { 7 - \sqrt { 6 } } { 7 + \sqrt { 6 } }$$

Aromātai

$$\frac{28\sqrt{6}}{43}\approx 1.595016577$$

Ngā Hipanga Rongoā Poto

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

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

Whakaarohia te \left(7-\sqrt{6}\right)\left(7+\sqrt{6}\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}.

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

Pūrua 7. Pūrua \sqrt{6}.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{49-6}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Tangohia te 6 i te 49, ka 43.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Whakareatia te 7+\sqrt{6} ki te 7+\sqrt{6}, ka \left(7+\sqrt{6}\right)^{2}.

$$\frac{\left(7+\sqrt{6}\right)^{2}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(7+\sqrt{6}\right)^{2}.

$$\frac{49+14\sqrt{6}+\left(\sqrt{6}\right)^{2}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{49+14\sqrt{6}+6}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Tāpirihia te 49 ki te 6, ka 55.

$$\frac{55+14\sqrt{6}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

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

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{\left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right)}$$

Whakaarohia te \left(7+\sqrt{6}\right)\left(7-\sqrt{6}\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}.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}$$

Pūrua 7. Pūrua \sqrt{6}.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{49-6}$$

Tangohia te 6 i te 49, ka 43.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{43}$$

Whakareatia te 7-\sqrt{6} ki te 7-\sqrt{6}, ka \left(7-\sqrt{6}\right)^{2}.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)^{2}}{43}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(7-\sqrt{6}\right)^{2}.

$$\frac{55+14\sqrt{6}}{43}-\frac{49-14\sqrt{6}+\left(\sqrt{6}\right)^{2}}{43}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{55+14\sqrt{6}}{43}-\frac{49-14\sqrt{6}+6}{43}$$

Tāpirihia te 49 ki te 6, ka 55.

$$\frac{55+14\sqrt{6}}{43}-\frac{55-14\sqrt{6}}{43}$$

Tā te mea he rite te tauraro o \frac{55+14\sqrt{6}}{43} me \frac{55-14\sqrt{6}}{43}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{55+14\sqrt{6}-\left(55-14\sqrt{6}\right)}{43}$$

Mahia ngā whakarea i roto o 55+14\sqrt{6}-\left(55-14\sqrt{6}\right).

$$\frac{55+14\sqrt{6}-55+14\sqrt{6}}{43}$$

Mahia ngā tātaitai i roto o 55+14\sqrt{6}-55+14\sqrt{6}.

$$\frac{28\sqrt{6}}{43}$$