Whakaoti i te 2/x+5/x+1-4/x

$$\frac{ 2 }{ x } + \frac{ 5 }{ x+1 } - \frac{ 4 }{ x }$$

Aromātai

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

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 x me x+1 ko x\left(x+1\right). Whakareatia \frac{2}{x} ki te \frac{x+1}{x+1}. Whakareatia \frac{5}{x+1} ki te \frac{x}{x}.

$$\frac{2\left(x+1\right)}{x\left(x+1\right)}+\frac{5x}{x\left(x+1\right)}-\frac{4}{x}$$

Tā te mea he rite te tauraro o \frac{2\left(x+1\right)}{x\left(x+1\right)} me \frac{5x}{x\left(x+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2\left(x+1\right)+5x}{x\left(x+1\right)}-\frac{4}{x}$$

Mahia ngā whakarea i roto o 2\left(x+1\right)+5x.

$$\frac{2x+2+5x}{x\left(x+1\right)}-\frac{4}{x}$$

Whakakotahitia ngā kupu rite i 2x+2+5x.

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

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

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

Tā te mea he rite te tauraro o \frac{7x+2}{x\left(x+1\right)} me \frac{4\left(x+1\right)}{x\left(x+1\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 7x+2-4\left(x+1\right).

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

Whakakotahitia ngā kupu rite i 7x+2-4x-4.

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

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

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

Kimi Pārōnaki e ai ki x

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

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 x me x+1 ko x\left(x+1\right). Whakareatia \frac{2}{x} ki te \frac{x+1}{x+1}. Whakareatia \frac{5}{x+1} ki te \frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x+1\right)}{x\left(x+1\right)}+\frac{5x}{x\left(x+1\right)}-\frac{4}{x})$$

Tā te mea he rite te tauraro o \frac{2\left(x+1\right)}{x\left(x+1\right)} me \frac{5x}{x\left(x+1\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x+1\right)+5x}{x\left(x+1\right)}-\frac{4}{x})$$

Mahia ngā whakarea i roto o 2\left(x+1\right)+5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+2+5x}{x\left(x+1\right)}-\frac{4}{x})$$

Whakakotahitia ngā kupu rite i 2x+2+5x.

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

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

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

Tā te mea he rite te tauraro o \frac{7x+2}{x\left(x+1\right)} me \frac{4\left(x+1\right)}{x\left(x+1\right)}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 7x+2-4\left(x+1\right).

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

Whakakotahitia ngā kupu rite i 7x+2-4x-4.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+1.

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

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.

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

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}.

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

Whakarūnātia.

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

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

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

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

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

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

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

Whakarūnātia.

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

Pahekotia ngā kīanga tau ōrite.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

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

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