Whakaoti i te x+5-3/x-2=

$$x + 5 - \frac { 3 } { x - 2 } =$$

Aromātai

$$\frac{x^{2}+3x-13}{x-2}$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x+5 ki te \frac{x-2}{x-2}.

$$\frac{\left(x+5\right)\left(x-2\right)}{x-2}-\frac{3}{x-2}$$

Tā te mea he rite te tauraro o \frac{\left(x+5\right)\left(x-2\right)}{x-2} me \frac{3}{x-2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\left(x+5\right)\left(x-2\right)-3}{x-2}$$

Mahia ngā whakarea i roto o \left(x+5\right)\left(x-2\right)-3.

$$\frac{x^{2}-2x+5x-10-3}{x-2}$$

Whakakotahitia ngā kupu rite i x^{2}-2x+5x-10-3.

$$\frac{x^{2}+3x-13}{x-2}$$

Kimi Pārōnaki e ai ki x

$$\frac{x^{2}-4x+7}{\left(x-2\right)^{2}}$$

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. Whakareatia x+5 ki te \frac{x-2}{x-2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x+5\right)\left(x-2\right)}{x-2}-\frac{3}{x-2})$$

Tā te mea he rite te tauraro o \frac{\left(x+5\right)\left(x-2\right)}{x-2} me \frac{3}{x-2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x+5\right)\left(x-2\right)-3}{x-2})$$

Mahia ngā whakarea i roto o \left(x+5\right)\left(x-2\right)-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-2x+5x-10-3}{x-2})$$

Whakakotahitia ngā kupu rite i x^{2}-2x+5x-10-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+3x-13}{x-2})$$

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.

$$\frac{\left(x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+3x^{1}-13)-\left(x^{2}+3x^{1}-13\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-2)}{\left(x^{1}-2\right)^{2}}$$

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}.

$$\frac{\left(x^{1}-2\right)\left(2x^{2-1}+3x^{1-1}\right)-\left(x^{2}+3x^{1}-13\right)x^{1-1}}{\left(x^{1}-2\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{1}-2\right)\left(2x^{1}+3x^{0}\right)-\left(x^{2}+3x^{1}-13\right)x^{0}}{\left(x^{1}-2\right)^{2}}$$

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

$$\frac{x^{1}\times 2x^{1}+x^{1}\times 3x^{0}-2\times 2x^{1}-2\times 3x^{0}-\left(x^{2}+3x^{1}-13\right)x^{0}}{\left(x^{1}-2\right)^{2}}$$

Whakareatia x^{2}+3x^{1}-13 ki te x^{0}.

$$\frac{x^{1}\times 2x^{1}+x^{1}\times 3x^{0}-2\times 2x^{1}-2\times 3x^{0}-\left(x^{2}x^{0}+3x^{1}x^{0}-13x^{0}\right)}{\left(x^{1}-2\right)^{2}}$$

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

$$\frac{2x^{1+1}+3x^{1}-2\times 2x^{1}-2\times 3x^{0}-\left(x^{2}+3x^{1}-13x^{0}\right)}{\left(x^{1}-2\right)^{2}}$$

Whakarūnātia.

$$\frac{2x^{2}+3x^{1}-4x^{1}-6x^{0}-\left(x^{2}+3x^{1}-13x^{0}\right)}{\left(x^{1}-2\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{x^{2}-4x^{1}+7x^{0}}{\left(x^{1}-2\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{x^{2}-4x+7x^{0}}{\left(x-2\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{x^{2}-4x+7\times 1}{\left(x-2\right)^{2}}$$

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

$$\frac{x^{2}-4x+7}{\left(x-2\right)^{2}}$$