Whakaoti i te 4*6/x^2-4x+3-3/3-x-4/x-1

$$\frac { 4 \times 6 } { x ^ { 2 } - 4 x + 3 } - \frac { 3 } { 3 - x } - \frac { 4 } { x - 1 }$$

Aromātai

$$\frac{x-33}{\left(3-x\right)\left(x-1\right)}$$

Ngā Hipanga Rongoā Poto

Whakareatia te 4 ki te 6, ka 24.

$$\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1}$$

Tauwehea te x^{2}-4x+3.

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1}$$

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

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Tā te mea he rite te tauraro o \frac{24}{\left(x-3\right)\left(x-1\right)} me \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Mahia ngā whakarea i roto o 24-3\left(-1\right)\left(x-1\right).

$$\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Whakakotahitia ngā kupu rite i 24+3x-3.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x-3\right)\left(x-1\right) me x-1 ko \left(x-3\right)\left(x-1\right). Whakareatia \frac{4}{x-1} ki te \frac{x-3}{x-3}.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

Tā te mea he rite te tauraro o \frac{21+3x}{\left(x-3\right)\left(x-1\right)} me \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

Mahia ngā whakarea i roto o 21+3x-4\left(x-3\right).

$$\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)}$$

Whakakotahitia ngā kupu rite i 21+3x-4x+12.

$$\frac{33-x}{\left(x-3\right)\left(x-1\right)}$$

Whakarohaina te \left(x-3\right)\left(x-1\right).

$$\frac{33-x}{x^{2}-4x+3}$$

Kimi Pārōnaki e ai ki x

$$\frac{x^{2}-66x+129}{x^{4}-8x^{3}+22x^{2}-24x+9}$$

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

Whakareatia te 4 ki te 6, ka 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1})$$

Tauwehea te x^{2}-4x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Tā te mea he rite te tauraro o \frac{24}{\left(x-3\right)\left(x-1\right)} me \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Mahia ngā whakarea i roto o 24-3\left(-1\right)\left(x-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Whakakotahitia ngā kupu rite i 24+3x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x-3\right)\left(x-1\right) me x-1 ko \left(x-3\right)\left(x-1\right). Whakareatia \frac{4}{x-1} ki te \frac{x-3}{x-3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

Tā te mea he rite te tauraro o \frac{21+3x}{\left(x-3\right)\left(x-1\right)} me \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

Mahia ngā whakarea i roto o 21+3x-4\left(x-3\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)})$$

Whakakotahitia ngā kupu rite i 21+3x-4x+12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{\left(x-3\right)\left(x-1\right)})$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-3 ki te x-1 ka whakakotahi i ngā kupu rite.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{x^{2}-4x+3})$$

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.

$$\frac{\left(x^{2}-4x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+33)-\left(-x^{1}+33\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}+3)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{1-1}-\left(-x^{1}+33\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Whakareatia x^{2}-4x^{1}+3 ki te -x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Whakareatia -x^{1}+33 ki te 2x^{1}-4x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-x^{1}\left(-4\right)x^{0}+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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

$$\frac{-x^{2}-4\left(-1\right)x^{1}+3\left(-1\right)x^{0}-\left(-2x^{1+1}-\left(-4x^{1}\right)+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Whakarūnātia.

$$\frac{-x^{2}+4x^{1}-3x^{0}-\left(-2x^{2}+4x^{1}+66x^{1}-132x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{x^{2}-66x^{1}+129x^{0}}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{x^{2}-66x+129x^{0}}{\left(x^{2}-4x+3\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{x^{2}-66x+129\times 1}{\left(x^{2}-4x+3\right)^{2}}$$

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

$$\frac{x^{2}-66x+129}{\left(x^{2}-4x+3\right)^{2}}$$