Whakaoti i te 2r/r^2-1-1/r+1

$$\frac { 2 r } { r ^ { 2 } - 1 } - \frac { 1 } { r + 1 }$$

Aromātai

$$\frac{1}{r-1}$$

Ngā Hipanga Rongoā Poto

Tauwehea te r^{2}-1.

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

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

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

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

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

Mahia ngā whakarea i roto o 2r-\left(r-1\right).

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

Whakakotahitia ngā kupu rite i 2r-r+1.

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

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

$$\frac{1}{r-1}$$

Kimi Pārōnaki e ai ki r

$$-\frac{1}{\left(r-1\right)^{2}}$$

Ngā Upane e Whakamahi ana i te Ture Mekameka

Tauwehea te r^{2}-1.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r}{\left(r-1\right)\left(r+1\right)}-\frac{1}{r+1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r}{\left(r-1\right)\left(r+1\right)}-\frac{r-1}{\left(r-1\right)\left(r+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r-\left(r-1\right)}{\left(r-1\right)\left(r+1\right)})$$

Mahia ngā whakarea i roto o 2r-\left(r-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r-r+1}{\left(r-1\right)\left(r+1\right)})$$

Whakakotahitia ngā kupu rite i 2r-r+1.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r+1}{\left(r-1\right)\left(r+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{r-1})$$

Mēnā ko F te hanganga o ngā pānga e rua e taea ana te pārōnaki f\left(u\right) me u=g\left(x\right), arā, mēnā ko F\left(x\right)=f\left(g\left(x\right)\right), ko te pārōnaki o F te pārōnaki o f e ai ki u whakareatia te pārōnaki o g e ai ki x, arā, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(r^{1}-1\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}r}(r^{1}-1)$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$-\left(r^{1}-1\right)^{-2}r^{1-1}$$

Whakarūnātia.

$$-r^{0}\left(r^{1}-1\right)^{-2}$$

Mō tētahi kupu t, t^{1}=t.

$$-r^{0}\left(r-1\right)^{-2}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$-\left(r-1\right)^{-2}$$