Whakaoti i te 4sqrt{3}-6-1/4sqrt{3-6}-1

$$4 \sqrt { 3 } - 6 - \frac { 1 } { 4 \sqrt { 3 } - 6 } - 1$$

Aromātai

$$\frac{11\sqrt{3}}{3}-\frac{15}{2}\approx -1.149147039$$

Ngā Hipanga Rongoā Poto

Whakangāwaritia te tauraro o \frac{1}{4\sqrt{3}-6} mā te whakarea i te taurunga me te tauraro ki te 4\sqrt{3}+6.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{\left(4\sqrt{3}-6\right)\left(4\sqrt{3}+6\right)}-1$$

Whakaarohia te \left(4\sqrt{3}-6\right)\left(4\sqrt{3}+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}.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{\left(4\sqrt{3}\right)^{2}-6^{2}}-1$$

Whakarohaina te \left(4\sqrt{3}\right)^{2}.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{4^{2}\left(\sqrt{3}\right)^{2}-6^{2}}-1$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{16\left(\sqrt{3}\right)^{2}-6^{2}}-1$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{16\times 3-6^{2}}-1$$

Whakareatia te 16 ki te 3, ka 48.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{48-6^{2}}-1$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{48-36}-1$$

Tangohia te 36 i te 48, ka 12.

$$4\sqrt{3}-6-\frac{4\sqrt{3}+6}{12}-1$$

Tangohia te 1 i te -6, ka -7.

$$4\sqrt{3}-7-\frac{4\sqrt{3}+6}{12}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4\sqrt{3}-7 ki te \frac{12}{12}.

$$\frac{12\left(4\sqrt{3}-7\right)}{12}-\frac{4\sqrt{3}+6}{12}$$

Tā te mea he rite te tauraro o \frac{12\left(4\sqrt{3}-7\right)}{12} me \frac{4\sqrt{3}+6}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{12\left(4\sqrt{3}-7\right)-\left(4\sqrt{3}+6\right)}{12}$$

Mahia ngā whakarea i roto o 12\left(4\sqrt{3}-7\right)-\left(4\sqrt{3}+6\right).

$$\frac{48\sqrt{3}-84-4\sqrt{3}-6}{12}$$

Mahia ngā tātaitai i roto o 48\sqrt{3}-84-4\sqrt{3}-6.

$$\frac{44\sqrt{3}-90}{12}$$

Tauwehe

$$\frac{22 \sqrt{3} - 45}{6} = -1.1491470389141167$$