Whakaoti i te 3/1-x+1/1+x-28/1-x^2

$$\frac { 3 } { 1 - x } + \frac { 1 } { 1 + x } - \frac { 28 } { 1 - x ^ { 2 } }$$

Aromātai

$$\frac{2\left(x-12\right)}{1-x^{2}}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 1-x me 1+x ko \left(x+1\right)\left(-x+1\right). Whakareatia \frac{3}{1-x} ki te \frac{x+1}{x+1}. Whakareatia \frac{1}{1+x} ki te \frac{-x+1}{-x+1}.

$$\frac{3\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)}+\frac{-x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}}$$

Tā te mea he rite te tauraro o \frac{3\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)} me \frac{-x+1}{\left(x+1\right)\left(-x+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3\left(x+1\right)-x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}}$$

Mahia ngā whakarea i roto o 3\left(x+1\right)-x+1.

$$\frac{3x+3-x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}}$$

Whakakotahitia ngā kupu rite i 3x+3-x+1.

$$\frac{2x+4}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}}$$

Tauwehea te 1-x^{2}.

$$\frac{2x+4}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{\left(x-1\right)\left(-x-1\right)}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x+1\right)\left(-x+1\right) me \left(x-1\right)\left(-x-1\right) ko \left(x-1\right)\left(x+1\right). Whakareatia \frac{2x+4}{\left(x+1\right)\left(-x+1\right)} ki te \frac{-1}{-1}. Whakareatia \frac{28}{\left(x-1\right)\left(-x-1\right)} ki te \frac{-1}{-1}.

$$\frac{-\left(2x+4\right)}{\left(x-1\right)\left(x+1\right)}-\frac{28\left(-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Tā te mea he rite te tauraro o \frac{-\left(2x+4\right)}{\left(x-1\right)\left(x+1\right)} me \frac{28\left(-1\right)}{\left(x-1\right)\left(x+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-\left(2x+4\right)-28\left(-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Mahia ngā whakarea i roto o -\left(2x+4\right)-28\left(-1\right).

$$\frac{-2x-4+28}{\left(x-1\right)\left(x+1\right)}$$

Whakakotahitia ngā kupu rite i -2x-4+28.

$$\frac{-2x+24}{\left(x-1\right)\left(x+1\right)}$$

Whakarohaina te \left(x-1\right)\left(x+1\right).

$$\frac{-2x+24}{x^{2}-1}$$

Kimi Pārōnaki e ai ki x

$$-\frac{2\left(-x^{2}+24x-1\right)}{\left(x^{2}-1\right)^{2}}$$

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Otinga

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 1-x me 1+x ko \left(x+1\right)\left(-x+1\right). Whakareatia \frac{3}{1-x} ki te \frac{x+1}{x+1}. Whakareatia \frac{1}{1+x} ki te \frac{-x+1}{-x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)}+\frac{-x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}})$$

Tā te mea he rite te tauraro o \frac{3\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)} me \frac{-x+1}{\left(x+1\right)\left(-x+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+1\right)-x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}})$$

Mahia ngā whakarea i roto o 3\left(x+1\right)-x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+3-x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}})$$

Whakakotahitia ngā kupu rite i 3x+3-x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+4}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{1-x^{2}})$$

Tauwehea te 1-x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+4}{\left(x+1\right)\left(-x+1\right)}-\frac{28}{\left(x-1\right)\left(-x-1\right)})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x+1\right)\left(-x+1\right) me \left(x-1\right)\left(-x-1\right) ko \left(x-1\right)\left(x+1\right). Whakareatia \frac{2x+4}{\left(x+1\right)\left(-x+1\right)} ki te \frac{-1}{-1}. Whakareatia \frac{28}{\left(x-1\right)\left(-x-1\right)} ki te \frac{-1}{-1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\left(2x+4\right)}{\left(x-1\right)\left(x+1\right)}-\frac{28\left(-1\right)}{\left(x-1\right)\left(x+1\right)})$$

Tā te mea he rite te tauraro o \frac{-\left(2x+4\right)}{\left(x-1\right)\left(x+1\right)} me \frac{28\left(-1\right)}{\left(x-1\right)\left(x+1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\left(2x+4\right)-28\left(-1\right)}{\left(x-1\right)\left(x+1\right)})$$

Mahia ngā whakarea i roto o -\left(2x+4\right)-28\left(-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x-4+28}{\left(x-1\right)\left(x+1\right)})$$

Whakakotahitia ngā kupu rite i -2x-4+28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x+24}{\left(x-1\right)\left(x+1\right)})$$

Whakaarohia te \left(x-1\right)\left(x+1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x+24}{x^{2}-1})$$

Mō ngā pānga e rua e taea ana te pārōnaki, ko te pārōnaki o te otinga o ngā pānga e rua ko te tauraro whakareatia ki te pārōnaki o te taurunga tango i te taurunga whakareatia ki te pārōnaki o te tauraro, ā, ka whakawehea te katoa ki te tauraro kua pūruatia.

$$\frac{\left(x^{2}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{1}+24)-\left(-2x^{1}+24\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-1)}{\left(x^{2}-1\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-1\right)\left(-2\right)x^{1-1}-\left(-2x^{1}+24\right)\times 2x^{2-1}}{\left(x^{2}-1\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(x^{2}-1\right)\left(-2\right)x^{0}-\left(-2x^{1}+24\right)\times 2x^{1}}{\left(x^{2}-1\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{2}\left(-2\right)x^{0}-\left(-2x^{0}\right)-\left(-2x^{1}\times 2x^{1}+24\times 2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$\frac{-2x^{2}-\left(-2x^{0}\right)-\left(-2\times 2x^{1+1}+24\times 2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{-2x^{2}+2x^{0}-\left(-4x^{2}+48x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{-2x^{2}+2x^{0}-\left(-4x^{2}\right)-48x^{1}}{\left(x^{2}-1\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-2-\left(-4\right)\right)x^{2}+2x^{0}-48x^{1}}{\left(x^{2}-1\right)^{2}}$$

Tango -4 mai i -2.

$$\frac{2x^{2}+2x^{0}-48x^{1}}{\left(x^{2}-1\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{2x^{2}+2x^{0}-48x}{\left(x^{2}-1\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{2x^{2}+2\times 1-48x}{\left(x^{2}-1\right)^{2}}$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$\frac{2x^{2}+2-48x}{\left(x^{2}-1\right)^{2}}$$