Whakaoti i te (2/x+3/x-5)

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

Aromātai

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

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-5 ko x\left(x-5\right). Whakareatia \frac{2}{x} ki te \frac{x-5}{x-5}. Whakareatia \frac{3}{x-5} ki te \frac{x}{x}.

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

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

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

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

$$\frac{2x-10+3x}{x\left(x-5\right)}$$

Whakakotahitia ngā kupu rite i 2x-10+3x.

$$\frac{5x-10}{x\left(x-5\right)}$$

Whakarohaina te x\left(x-5\right).

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

Kimi Pārōnaki e ai ki x

$$\frac{5\left(-x^{2}+4x-10\right)}{\left(x\left(x-5\right)\right)^{2}}$$

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-5 ko x\left(x-5\right). Whakareatia \frac{2}{x} ki te \frac{x-5}{x-5}. Whakareatia \frac{3}{x-5} ki te \frac{x}{x}.

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

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

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

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

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

Whakakotahitia ngā kupu rite i 2x-10+3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-10}{x\left(x-5\right)})$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-5.

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

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.

$$\frac{\left(x^{2}-5x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1}-10)-\left(5x^{1}-10\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-5x^{1})}{\left(x^{2}-5x^{1}\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-5x^{1}\right)\times 5x^{1-1}-\left(5x^{1}-10\right)\left(2x^{2-1}-5x^{1-1}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-5x^{1}\right)\times 5x^{0}-\left(5x^{1}-10\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Whakareatia x^{2}-5x^{1} ki te 5x^{0}.

$$\frac{x^{2}\times 5x^{0}-5x^{1}\times 5x^{0}-\left(5x^{1}-10\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Whakareatia 5x^{1}-10 ki te 2x^{1}-5x^{0}.

$$\frac{x^{2}\times 5x^{0}-5x^{1}\times 5x^{0}-\left(5x^{1}\times 2x^{1}+5x^{1}\left(-5\right)x^{0}-10\times 2x^{1}-10\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

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

$$\frac{5x^{2}-5\times 5x^{1}-\left(5\times 2x^{1+1}+5\left(-5\right)x^{1}-10\times 2x^{1}-10\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Whakarūnātia.

$$\frac{5x^{2}-25x^{1}-\left(10x^{2}-25x^{1}-20x^{1}+50x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-5x^{2}+20x^{1}-50x^{0}}{\left(x^{2}-5x^{1}\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-5x^{2}+20x-50x^{0}}{\left(x^{2}-5x\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-5x^{2}+20x-50}{\left(x^{2}-5x\right)^{2}}$$