Whakaoti i te x/x^2+10x+24-4/x^2+6x+8

$$\frac { x } { x ^ { 2 } + 10 x + 24 } - \frac { 4 } { x ^ { 2 } + 6 x + 8 }$$

Aromātai

$$\frac{x-6}{\left(x+2\right)\left(x+6\right)}$$

Ngā Hipanga Rongoā Poto

Tauwehea te x^{2}+10x+24. Tauwehea te x^{2}+6x+8.

$$\frac{x}{\left(x+4\right)\left(x+6\right)}-\frac{4}{\left(x+2\right)\left(x+4\right)}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x+4\right)\left(x+6\right) me \left(x+2\right)\left(x+4\right) ko \left(x+2\right)\left(x+4\right)\left(x+6\right). Whakareatia \frac{x}{\left(x+4\right)\left(x+6\right)} ki te \frac{x+2}{x+2}. Whakareatia \frac{4}{\left(x+2\right)\left(x+4\right)} ki te \frac{x+6}{x+6}.

$$\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}-\frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

Tā te mea he rite te tauraro o \frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} me \frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(x+2\right)-4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

Mahia ngā whakarea i roto o x\left(x+2\right)-4\left(x+6\right).

$$\frac{x^{2}+2x-4x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

Whakakotahitia ngā kupu rite i x^{2}+2x-4x-24.

$$\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}.

$$\frac{\left(x-6\right)\left(x+4\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

Me whakakore tahi te x+4 i te taurunga me te tauraro.

$$\frac{x-6}{\left(x+2\right)\left(x+6\right)}$$

Whakarohaina te \left(x+2\right)\left(x+6\right).

$$\frac{x-6}{x^{2}+8x+12}$$

Kimi Pārōnaki e ai ki x

$$\frac{60+12x-x^{2}}{x^{4}+16x^{3}+88x^{2}+192x+144}$$

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

Tauwehea te x^{2}+10x+24. Tauwehea te x^{2}+6x+8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x+4\right)\left(x+6\right)}-\frac{4}{\left(x+2\right)\left(x+4\right)})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(x+4\right)\left(x+6\right) me \left(x+2\right)\left(x+4\right) ko \left(x+2\right)\left(x+4\right)\left(x+6\right). Whakareatia \frac{x}{\left(x+4\right)\left(x+6\right)} ki te \frac{x+2}{x+2}. Whakareatia \frac{4}{\left(x+2\right)\left(x+4\right)} ki te \frac{x+6}{x+6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}-\frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

Tā te mea he rite te tauraro o \frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} me \frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+2\right)-4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

Mahia ngā whakarea i roto o x\left(x+2\right)-4\left(x+6\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+2x-4x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

Whakakotahitia ngā kupu rite i x^{2}+2x-4x-24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-6\right)\left(x+4\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

Me whakakore tahi te x+4 i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-6}{\left(x+2\right)\left(x+6\right)})$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x+6 ka whakakotahi i ngā kupu rite.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-6}{x^{2}+8x+12})$$

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.

$$\frac{\left(x^{2}+8x^{1}+12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-6)-\left(x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+8x^{1}+12)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

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}.

$$\frac{\left(x^{2}+8x^{1}+12\right)x^{1-1}-\left(x^{1}-6\right)\left(2x^{2-1}+8x^{1-1}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}+8x^{1}+12\right)x^{0}-\left(x^{1}-6\right)\left(2x^{1}+8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Whakareatia x^{2}+8x^{1}+12 ki te x^{0}.

$$\frac{x^{2}x^{0}+8x^{1}x^{0}+12x^{0}-\left(x^{1}-6\right)\left(2x^{1}+8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Whakareatia x^{1}-6 ki te 2x^{1}+8x^{0}.

$$\frac{x^{2}x^{0}+8x^{1}x^{0}+12x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\times 8x^{0}-6\times 2x^{1}-6\times 8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

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

$$\frac{x^{2}+8x^{1}+12x^{0}-\left(2x^{1+1}+8x^{1}-6\times 2x^{1}-6\times 8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Whakarūnātia.

$$\frac{x^{2}+8x^{1}+12x^{0}-\left(2x^{2}+8x^{1}-12x^{1}-48x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-x^{2}+12x^{1}+60x^{0}}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-x^{2}+12x+60x^{0}}{\left(x^{2}+8x+12\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-x^{2}+12x+60\times 1}{\left(x^{2}+8x+12\right)^{2}}$$

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

$$\frac{-x^{2}+12x+60}{\left(x^{2}+8x+12\right)^{2}}$$