Whakaoti i te (1/1+x+2x/1-x^2)*(1/x-1)

$$( \frac { 1 } { 1 + x } + \frac { 2 x } { 1 - x ^ { 2 } } ) \cdot ( \frac { 1 } { x } - 1 )$$

Aromātai

$$\frac{1}{x}$$

Ngā Hipanga Rongoā Poto

Tauwehea te 1-x^{2}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i x-1-2x.

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

Unuhia te tohu tōraro i roto o -x-1.

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

Me whakakore tahi te x+1 i te taurunga me te tauraro.

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

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

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

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

$$\frac{-1}{x-1}\times \frac{1-x}{x}$$

Me whakarea te \frac{-1}{x-1} ki te \frac{1-x}{x} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Unuhia te tohu tōraro i roto o 1-x.

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

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

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

Whakareatia te -1 ki te -1, ka 1.

$$\frac{1}{x}$$

Whakaroha

$$\frac{1}{x}$$

Ngā Hipanga Rongoā Poto

Tauwehea te 1-x^{2}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i x-1-2x.

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

Unuhia te tohu tōraro i roto o -x-1.

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

Me whakakore tahi te x+1 i te taurunga me te tauraro.

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

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

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

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

$$\frac{-1}{x-1}\times \frac{1-x}{x}$$

Me whakarea te \frac{-1}{x-1} ki te \frac{1-x}{x} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Unuhia te tohu tōraro i roto o 1-x.

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

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

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

Whakareatia te -1 ki te -1, ka 1.

$$\frac{1}{x}$$