Whakaoti i te 6m+mn/4mdivn^2-36

$$\frac { 6 m + m n } { 4 m } \div n ^ { 2 } - 36$$

Aromātai

$$-36+\frac{1}{4n}+\frac{3}{2n^{2}}$$

Ngā Hipanga Rongoā Poto

Tuhia te \frac{\frac{6m+mn}{4m}}{n^{2}} hei hautanga kotahi.

$$\frac{6m+mn}{4mn^{2}}-36$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{6m+mn}{4mn^{2}}.

$$\frac{m\left(n+6\right)}{4mn^{2}}-36$$

Me whakakore tahi te m i te taurunga me te tauraro.

$$\frac{n+6}{4n^{2}}-36$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 36 ki te \frac{4n^{2}}{4n^{2}}.

$$\frac{n+6}{4n^{2}}-\frac{36\times 4n^{2}}{4n^{2}}$$

Tā te mea he rite te tauraro o \frac{n+6}{4n^{2}} me \frac{36\times 4n^{2}}{4n^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{n+6-36\times 4n^{2}}{4n^{2}}$$

Mahia ngā whakarea i roto o n+6-36\times 4n^{2}.

$$\frac{n+6-144n^{2}}{4n^{2}}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{n+6-144n^{2}}{4n^{2}}.

$$\frac{-144\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{4n^{2}}$$

Me whakakore tahi te 4 i te taurunga me te tauraro.

$$\frac{-36\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Hei kimi i te tauaro o -\frac{1}{288}\sqrt{3457}+\frac{1}{288}, kimihia te tauaro o ia taurangi.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Hei kimi i te tauaro o \frac{1}{288}\sqrt{3457}+\frac{1}{288}, kimihia te tauaro o ia taurangi.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -36 ki te n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}.

$$\frac{\left(-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8} ki te n-\frac{1}{288}\sqrt{3457}-\frac{1}{288} ka whakakotahi i ngā kupu rite.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\left(\sqrt{3457}\right)^{2}-\frac{1}{2304}}{n^{2}}$$

Ko te pūrua o \sqrt{3457} ko 3457.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\times 3457-\frac{1}{2304}}{n^{2}}$$

Whakareatia te \frac{1}{2304} ki te 3457, ka \frac{3457}{2304}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3457}{2304}-\frac{1}{2304}}{n^{2}}$$

Tangohia te \frac{1}{2304} i te \frac{3457}{2304}, ka \frac{3}{2}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3}{2}}{n^{2}}$$

Whakaroha

$$-36+\frac{1}{4n}+\frac{3}{2n^{2}}$$

Ngā Hipanga Rongoā Poto

Tuhia te \frac{\frac{6m+mn}{4m}}{n^{2}} hei hautanga kotahi.

$$\frac{6m+mn}{4mn^{2}}-36$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{6m+mn}{4mn^{2}}.

$$\frac{m\left(n+6\right)}{4mn^{2}}-36$$

Me whakakore tahi te m i te taurunga me te tauraro.

$$\frac{n+6}{4n^{2}}-36$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 36 ki te \frac{4n^{2}}{4n^{2}}.

$$\frac{n+6}{4n^{2}}-\frac{36\times 4n^{2}}{4n^{2}}$$

Tā te mea he rite te tauraro o \frac{n+6}{4n^{2}} me \frac{36\times 4n^{2}}{4n^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{n+6-36\times 4n^{2}}{4n^{2}}$$

Mahia ngā whakarea i roto o n+6-36\times 4n^{2}.

$$\frac{n+6-144n^{2}}{4n^{2}}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{n+6-144n^{2}}{4n^{2}}.

$$\frac{-144\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{4n^{2}}$$

Me whakakore tahi te 4 i te taurunga me te tauraro.

$$\frac{-36\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Hei kimi i te tauaro o -\frac{1}{288}\sqrt{3457}+\frac{1}{288}, kimihia te tauaro o ia taurangi.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Hei kimi i te tauaro o \frac{1}{288}\sqrt{3457}+\frac{1}{288}, kimihia te tauaro o ia taurangi.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -36 ki te n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}.

$$\frac{\left(-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8} ki te n-\frac{1}{288}\sqrt{3457}-\frac{1}{288} ka whakakotahi i ngā kupu rite.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\left(\sqrt{3457}\right)^{2}-\frac{1}{2304}}{n^{2}}$$

Ko te pūrua o \sqrt{3457} ko 3457.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\times 3457-\frac{1}{2304}}{n^{2}}$$

Whakareatia te \frac{1}{2304} ki te 3457, ka \frac{3457}{2304}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3457}{2304}-\frac{1}{2304}}{n^{2}}$$

Tangohia te \frac{1}{2304} i te \frac{3457}{2304}, ka \frac{3}{2}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3}{2}}{n^{2}}$$