Whakaoti i te 12left(120-175right)/12+frac{2*10{sqrt{3}}}

$$\frac{ 12 \left( 120-175 \right) }{ 12+ \frac{ 2 \cdot 10 }{ \sqrt{ 3 } } }$$

Aromātai

$$\frac{825\sqrt{3}-1485}{2}\approx -28.029041878$$

Ngā Hipanga Rongoā Poto

Tangohia te 175 i te 120, ka -55.

$$\frac{12\left(-55\right)}{12+\frac{2\times 10}{\sqrt{3}}}$$

Whakareatia te 12 ki te -55, ka -660.

$$\frac{-660}{12+\frac{2\times 10}{\sqrt{3}}}$$

Whakareatia te 2 ki te 10, ka 20.

$$\frac{-660}{12+\frac{20}{\sqrt{3}}}$$

Whakangāwaritia te tauraro o \frac{20}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{-660}{12+\frac{20\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{-660}{12+\frac{20\sqrt{3}}{3}}$$

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

$$\frac{-660}{\frac{12\times 3}{3}+\frac{20\sqrt{3}}{3}}$$

Tā te mea he rite te tauraro o \frac{12\times 3}{3} me \frac{20\sqrt{3}}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-660}{\frac{12\times 3+20\sqrt{3}}{3}}$$

Mahia ngā whakarea i roto o 12\times 3+20\sqrt{3}.

$$\frac{-660}{\frac{36+20\sqrt{3}}{3}}$$

Whakawehe -660 ki te \frac{36+20\sqrt{3}}{3} mā te whakarea -660 ki te tau huripoki o \frac{36+20\sqrt{3}}{3}.

$$\frac{-660\times 3}{36+20\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{-660\times 3}{36+20\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 36-20\sqrt{3}.

$$\frac{-660\times 3\left(36-20\sqrt{3}\right)}{\left(36+20\sqrt{3}\right)\left(36-20\sqrt{3}\right)}$$

Whakaarohia te \left(36+20\sqrt{3}\right)\left(36-20\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}.

$$\frac{-660\times 3\left(36-20\sqrt{3}\right)}{36^{2}-\left(20\sqrt{3}\right)^{2}}$$

Whakareatia te -660 ki te 3, ka -1980.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{36^{2}-\left(20\sqrt{3}\right)^{2}}$$

Tātaihia te 36 mā te pū o 2, kia riro ko 1296.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-\left(20\sqrt{3}\right)^{2}}$$

Whakarohaina te \left(20\sqrt{3}\right)^{2}.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-20^{2}\left(\sqrt{3}\right)^{2}}$$

Tātaihia te 20 mā te pū o 2, kia riro ko 400.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-400\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-400\times 3}$$

Whakareatia te 400 ki te 3, ka 1200.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{1296-1200}$$

Tangohia te 1200 i te 1296, ka 96.

$$\frac{-1980\left(36-20\sqrt{3}\right)}{96}$$

Whakawehea te -1980\left(36-20\sqrt{3}\right) ki te 96, kia riro ko -\frac{165}{8}\left(36-20\sqrt{3}\right).

$$-\frac{165}{8}\left(36-20\sqrt{3}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{165}{8} ki te 36-20\sqrt{3}.

$$-\frac{165}{8}\times 36-\frac{165}{8}\left(-20\right)\sqrt{3}$$

Tuhia te -\frac{165}{8}\times 36 hei hautanga kotahi.

$$\frac{-165\times 36}{8}-\frac{165}{8}\left(-20\right)\sqrt{3}$$

Whakareatia te -165 ki te 36, ka -5940.

$$\frac{-5940}{8}-\frac{165}{8}\left(-20\right)\sqrt{3}$$

Whakahekea te hautanga \frac{-5940}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{1485}{2}-\frac{165}{8}\left(-20\right)\sqrt{3}$$

Tuhia te -\frac{165}{8}\left(-20\right) hei hautanga kotahi.

$$-\frac{1485}{2}+\frac{-165\left(-20\right)}{8}\sqrt{3}$$

Whakareatia te -165 ki te -20, ka 3300.

$$-\frac{1485}{2}+\frac{3300}{8}\sqrt{3}$$

Whakahekea te hautanga \frac{3300}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{1485}{2}+\frac{825}{2}\sqrt{3}$$

Tauwehe

$$\frac{165 {(5 \sqrt{3} - 9)}}{2} = -28.029041877838196$$