Whakaoti i te frac{{left(sqrt{3}+1+sqrt{3}-1right)}^2}{{left(sqrt{3}+1right)}^2-{left(sqrt{3}-1right)}^2}

$$\frac{ { \left( \sqrt{ 3 } +1+ \sqrt{ 3 } -1 \right) }^{ 2 } }{ { \left( \sqrt{ 3 } +1 \right) }^{ 2 } - { \left( \sqrt{ 3 } -1 \right) }^{ 2 } }$$

Aromātai

$$\sqrt{3}\approx 1.732050808$$

Ngā Upane Otinga

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

$$\frac{\left(2\sqrt{3}+1-1\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Tangohia te 1 i te 1, ka 0.

$$\frac{\left(2\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

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

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4\times 3}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{3}+1\right)^{2}.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Tāpirihia te 3 ki te 1, ka 4.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{3}-1\right)^{2}.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

Tāpirihia te 3 ki te 1, ka 4.

$$\frac{12}{4+2\sqrt{3}-\left(4-2\sqrt{3}\right)}$$

Hei kimi i te tauaro o 4-2\sqrt{3}, kimihia te tauaro o ia taurangi.

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

Tangohia te 4 i te 4, ka 0.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

Pahekotia te 2\sqrt{3} me 2\sqrt{3}, ka 4\sqrt{3}.

$$\frac{12}{4\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{12}{4\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Me whakakore tahi te 3\times 4 i te taurunga me te tauraro.

$$\sqrt{3}$$

Whakaroha

$$\sqrt{3} = 1.732050808$$

Ngā Upane Otinga

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

$$\frac{\left(2\sqrt{3}+1-1\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Tangohia te 1 i te 1, ka 0.

$$\frac{\left(2\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

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

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4\times 3}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{3}+1\right)^{2}.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Tāpirihia te 3 ki te 1, ka 4.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{3}-1\right)^{2}.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

Tāpirihia te 3 ki te 1, ka 4.

$$\frac{12}{4+2\sqrt{3}-\left(4-2\sqrt{3}\right)}$$

Hei kimi i te tauaro o 4-2\sqrt{3}, kimihia te tauaro o ia taurangi.

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

Tangohia te 4 i te 4, ka 0.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

Pahekotia te 2\sqrt{3} me 2\sqrt{3}, ka 4\sqrt{3}.

$$\frac{12}{4\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{12}{4\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Me whakakore tahi te 3\times 4 i te taurunga me te tauraro.

$$\sqrt{3}$$