Whakaoti i te 3/2-sqrt{3}+4/sqrt{3+1}

$$\frac { 3 } { 2 - \sqrt { 3 } } + \frac { 4 } { \sqrt { 3 } + 1 }$$

Aromātai

$$5\sqrt{3}+4\approx 12.660254038$$

Ngā Upane Otinga

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

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

Whakaarohia te \left(2-\sqrt{3}\right)\left(2+\sqrt{3}\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}.

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

Pūrua 2. Pūrua \sqrt{3}.

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

Tangohia te 3 i te 4, ka 1.

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

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

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

Whakangāwaritia te tauraro o \frac{4}{\sqrt{3}+1} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}-1.

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

Whakaarohia te \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\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}.

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

Pūrua \sqrt{3}. Pūrua 1.

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

Tangohia te 1 i te 3, ka 2.

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

Whakawehea te 4\left(\sqrt{3}-1\right) ki te 2, kia riro ko 2\left(\sqrt{3}-1\right).

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te \sqrt{3}-1.

$$6+3\sqrt{3}+2\sqrt{3}-2$$

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

$$6+5\sqrt{3}-2$$

Tangohia te 2 i te 6, ka 4.

$$4+5\sqrt{3}$$