Whakaoti i te 1/2x-7/14+12/16x^2

$$\frac { 1 } { 2 x } - \frac { 7 } { 14 } + \frac { 12 } { 16 x ^ { 2 } }$$

Aromātai

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

Ngā Hipanga Rongoā Poto

Whakahekea te hautanga \frac{7}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{1}{2x}-\frac{1}{2}+\frac{12}{16x^{2}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2x me 2 ko 2x. Whakareatia \frac{1}{2} ki te \frac{x}{x}.

$$\frac{1}{2x}-\frac{x}{2x}+\frac{12}{16x^{2}}$$

Tā te mea he rite te tauraro o \frac{1}{2x} me \frac{x}{2x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1-x}{2x}+\frac{12}{16x^{2}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2x me 16x^{2} ko 16x^{2}. Whakareatia \frac{1-x}{2x} ki te \frac{8x}{8x}.

$$\frac{\left(1-x\right)\times 8x}{16x^{2}}+\frac{12}{16x^{2}}$$

Tā te mea he rite te tauraro o \frac{\left(1-x\right)\times 8x}{16x^{2}} me \frac{12}{16x^{2}}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(1-x\right)\times 8x+12}{16x^{2}}$$

Mahia ngā whakarea i roto o \left(1-x\right)\times 8x+12.

$$\frac{8x-8x^{2}+12}{16x^{2}}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{8x-8x^{2}+12}{16x^{2}}.

$$\frac{-2\times 4\left(x-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}{16x^{2}}$$

Me whakakore tahi te 2\times 4 i te taurunga me te tauraro.

$$\frac{-\left(x-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}{2x^{2}}$$

Me whakakore tahi te -1 i te taurunga me te tauraro.

$$\frac{\left(x-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}{-2x^{2}}$$

Hei kimi i te tauaro o -\frac{1}{2}\sqrt{7}+\frac{1}{2}, kimihia te tauaro o ia taurangi.

$$\frac{\left(x+\frac{1}{2}\sqrt{7}-\frac{1}{2}\right)\left(x-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}{-2x^{2}}$$

Hei kimi i te tauaro o \frac{1}{2}\sqrt{7}+\frac{1}{2}, kimihia te tauaro o ia taurangi.

$$\frac{\left(x+\frac{1}{2}\sqrt{7}-\frac{1}{2}\right)\left(x-\frac{1}{2}\sqrt{7}-\frac{1}{2}\right)}{-2x^{2}}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+\frac{1}{2}\sqrt{7}-\frac{1}{2} ki te x-\frac{1}{2}\sqrt{7}-\frac{1}{2} ka whakakotahi i ngā kupu rite.

$$\frac{x^{2}-x-\frac{1}{4}\left(\sqrt{7}\right)^{2}+\frac{1}{4}}{-2x^{2}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{x^{2}-x-\frac{1}{4}\times 7+\frac{1}{4}}{-2x^{2}}$$

Whakareatia te -\frac{1}{4} ki te 7, ka -\frac{7}{4}.

$$\frac{x^{2}-x-\frac{7}{4}+\frac{1}{4}}{-2x^{2}}$$

Tāpirihia te -\frac{7}{4} ki te \frac{1}{4}, ka -\frac{3}{2}.

$$\frac{x^{2}-x-\frac{3}{2}}{-2x^{2}}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea.

$$\frac{\frac{1}{2}\times 2\left(x-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}{-2x^{2}}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{\frac{1}{2}\left(x-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}{-x^{2}}$$

Me whakaroha te kīanga.

$$\frac{\frac{1}{2}x^{2}-\frac{1}{2}x-\frac{3}{4}}{-x^{2}}$$

Tauwehe

$$-\frac{\frac{1}{2}\left(x-\frac{1-\sqrt{7}}{2}\right)\left(x-\frac{\sqrt{7}+1}{2}\right)}{x^{2}}$$