Whakaoti i te [1.5-(x^{4}-frac{x^{4}+1}{x^{2}+1})*frac{(x^{2}+1)(x-4)}{x^7+6x^6-x-6}]:x^2+29x+78/3x^2+12x-36=

$$[ 1.5 - ( x ^ { 4 } - \frac { x ^ { 4 } + 1 } { x ^ { 2 } + 1 } ) \cdot \frac { ( x ^ { 2 } + 1 ) ( x - 4 ) } { x ^ { 7 } + 6 x ^ { 6 } - x - 6 } ] : \frac { x ^ { 2 } + 29 x + 78 } { 3 x ^ { 2 } + 12 x - 36 } =$$

Aromātai

$$\frac{3\left(x-2\right)}{2\left(x+3\right)}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{4} ki te \frac{x^{2}+1}{x^{2}+1}.

$$\frac{1.5-\left(\frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1}-\frac{x^{4}+1}{x^{2}+1}\right)\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Tā te mea he rite te tauraro o \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} me \frac{x^{4}+1}{x^{2}+1}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1.5-\frac{x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right)}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Mahia ngā whakarea i roto o x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

$$\frac{1.5-\frac{x^{6}+x^{4}-x^{4}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Whakakotahitia ngā kupu rite i x^{6}+x^{4}-x^{4}-1.

$$\frac{1.5-\frac{x^{6}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakarea te \frac{x^{6}-1}{x^{2}+1} ki te \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1.5-\frac{\left(x^{6}-1\right)\left(x^{2}+1\right)\left(x-4\right)}{\left(x^{2}+1\right)\left(x^{7}+6x^{6}-x-6\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakakore tahi te x^{2}+1 i te taurunga me te tauraro.

$$\frac{1.5-\frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}.

$$\frac{1.5-\frac{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+6\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakakore tahi te \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) i te taurunga me te tauraro.

$$\frac{1.5-\frac{x-4}{x+6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Whakawehe 1.5-\frac{x-4}{x+6} ki te \frac{x^{2}+29x+78}{3x^{2}+12x-36} mā te whakarea 1.5-\frac{x-4}{x+6} ki te tau huripoki o \frac{x^{2}+29x+78}{3x^{2}+12x-36}.

$$\frac{\left(1.5-\frac{x-4}{x+6}\right)\left(3x^{2}+12x-36\right)}{x^{2}+29x+78}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1.5-\frac{x-4}{x+6} ki te 3x^{2}+12x-36.

$$\frac{4.5x^{2}+18x-54-3\times \frac{x-4}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te -3\times \frac{x-4}{x+6} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te \frac{-3\left(x-4\right)}{x+6}x^{2} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te -12\times \frac{x-4}{x+6} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te \frac{-12\left(x-4\right)}{x+6}x hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te 36\times \frac{x-4}{x+6} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 18x-54 ki te \frac{x+6}{x+6}.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)}{x+6}+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tā te mea he rite te tauraro o \frac{\left(18x-54\right)\left(x+6\right)}{x+6} me \frac{-3\left(x-4\right)x^{2}}{x+6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Mahia ngā whakarea i roto o \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

$$\frac{4.5x^{2}+\frac{18x^{2}+108x-54x-324-3x^{3}+12x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Whakakotahitia ngā kupu rite i 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tā te mea he rite te tauraro o \frac{30x^{2}+54x-324-3x^{3}}{x+6} me \frac{-12\left(x-4\right)x}{x+6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Mahia ngā whakarea i roto o 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12x^{2}+48x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Whakakotahitia ngā kupu rite i 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tā te mea he rite te tauraro o \frac{18x^{2}+102x-324-3x^{3}}{x+6} me \frac{36\left(x-4\right)}{x+6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Mahia ngā whakarea i roto o 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36x-144}{x+6}}{x^{2}+29x+78}$$

Whakakotahitia ngā kupu rite i 18x^{2}+102x-324-3x^{3}+36x-144.

$$\frac{4.5x^{2}+\frac{18x^{2}+138x-468-3x^{3}}{x+6}}{x^{2}+29x+78}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{18x^{2}+138x-468-3x^{3}}{x+6}.

$$\frac{4.5x^{2}+\frac{3\left(x+6\right)\left(-x^{2}+12x-26\right)}{x+6}}{x^{2}+29x+78}$$

Me whakakore tahi te x+6 i te taurunga me te tauraro.

$$\frac{4.5x^{2}+3\left(-x^{2}+12x-26\right)}{x^{2}+29x+78}$$

Me whakaroha te kīanga.

$$\frac{4.5x^{2}-3x^{2}+36x-78}{x^{2}+29x+78}$$

Pahekotia te 4.5x^{2} me -3x^{2}, ka 1.5x^{2}.

$$\frac{1.5x^{2}+36x-78}{x^{2}+29x+78}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea.

$$\frac{3\left(\frac{1}{2}x-1\right)\left(x+26\right)}{\left(x+3\right)\left(x+26\right)}$$

Me whakakore tahi te x+26 i te taurunga me te tauraro.

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

Me whakaroha te kīanga.

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

Whakaroha

$$\frac{3\left(x-2\right)}{2\left(x+3\right)}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{4} ki te \frac{x^{2}+1}{x^{2}+1}.

$$\frac{1.5-\left(\frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1}-\frac{x^{4}+1}{x^{2}+1}\right)\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Tā te mea he rite te tauraro o \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} me \frac{x^{4}+1}{x^{2}+1}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1.5-\frac{x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right)}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Mahia ngā whakarea i roto o x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

$$\frac{1.5-\frac{x^{6}+x^{4}-x^{4}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Whakakotahitia ngā kupu rite i x^{6}+x^{4}-x^{4}-1.

$$\frac{1.5-\frac{x^{6}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakarea te \frac{x^{6}-1}{x^{2}+1} ki te \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1.5-\frac{\left(x^{6}-1\right)\left(x^{2}+1\right)\left(x-4\right)}{\left(x^{2}+1\right)\left(x^{7}+6x^{6}-x-6\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakakore tahi te x^{2}+1 i te taurunga me te tauraro.

$$\frac{1.5-\frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}.

$$\frac{1.5-\frac{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+6\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Me whakakore tahi te \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) i te taurunga me te tauraro.

$$\frac{1.5-\frac{x-4}{x+6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Whakawehe 1.5-\frac{x-4}{x+6} ki te \frac{x^{2}+29x+78}{3x^{2}+12x-36} mā te whakarea 1.5-\frac{x-4}{x+6} ki te tau huripoki o \frac{x^{2}+29x+78}{3x^{2}+12x-36}.

$$\frac{\left(1.5-\frac{x-4}{x+6}\right)\left(3x^{2}+12x-36\right)}{x^{2}+29x+78}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1.5-\frac{x-4}{x+6} ki te 3x^{2}+12x-36.

$$\frac{4.5x^{2}+18x-54-3\times \frac{x-4}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te -3\times \frac{x-4}{x+6} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te \frac{-3\left(x-4\right)}{x+6}x^{2} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te -12\times \frac{x-4}{x+6} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te \frac{-12\left(x-4\right)}{x+6}x hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Tuhia te 36\times \frac{x-4}{x+6} hei hautanga kotahi.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 18x-54 ki te \frac{x+6}{x+6}.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)}{x+6}+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tā te mea he rite te tauraro o \frac{\left(18x-54\right)\left(x+6\right)}{x+6} me \frac{-3\left(x-4\right)x^{2}}{x+6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Mahia ngā whakarea i roto o \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

$$\frac{4.5x^{2}+\frac{18x^{2}+108x-54x-324-3x^{3}+12x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Whakakotahitia ngā kupu rite i 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tā te mea he rite te tauraro o \frac{30x^{2}+54x-324-3x^{3}}{x+6} me \frac{-12\left(x-4\right)x}{x+6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Mahia ngā whakarea i roto o 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12x^{2}+48x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Whakakotahitia ngā kupu rite i 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tā te mea he rite te tauraro o \frac{18x^{2}+102x-324-3x^{3}}{x+6} me \frac{36\left(x-4\right)}{x+6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Mahia ngā whakarea i roto o 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36x-144}{x+6}}{x^{2}+29x+78}$$

Whakakotahitia ngā kupu rite i 18x^{2}+102x-324-3x^{3}+36x-144.

$$\frac{4.5x^{2}+\frac{18x^{2}+138x-468-3x^{3}}{x+6}}{x^{2}+29x+78}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{18x^{2}+138x-468-3x^{3}}{x+6}.

$$\frac{4.5x^{2}+\frac{3\left(x+6\right)\left(-x^{2}+12x-26\right)}{x+6}}{x^{2}+29x+78}$$

Me whakakore tahi te x+6 i te taurunga me te tauraro.

$$\frac{4.5x^{2}+3\left(-x^{2}+12x-26\right)}{x^{2}+29x+78}$$

Me whakaroha te kīanga.

$$\frac{4.5x^{2}-3x^{2}+36x-78}{x^{2}+29x+78}$$

Pahekotia te 4.5x^{2} me -3x^{2}, ka 1.5x^{2}.

$$\frac{1.5x^{2}+36x-78}{x^{2}+29x+78}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea.

$$\frac{3\left(\frac{1}{2}x-1\right)\left(x+26\right)}{\left(x+3\right)\left(x+26\right)}$$

Me whakakore tahi te x+26 i te taurunga me te tauraro.

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

Me whakaroha te kīanga.

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