Whakaoti i te 4/2r+5+3/5r-2

$$\frac { 4 } { 2 r + 5 } + \frac { 3 } { 5 r - 2 }$$

Aromātai

$$\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)}$$

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 2r+5 me 5r-2 ko \left(5r-2\right)\left(2r+5\right). Whakareatia \frac{4}{2r+5} ki te \frac{5r-2}{5r-2}. Whakareatia \frac{3}{5r-2} ki te \frac{2r+5}{2r+5}.

$$\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)}+\frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}$$

Tā te mea he rite te tauraro o \frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)} me \frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4\left(5r-2\right)+3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}$$

Mahia ngā whakarea i roto o 4\left(5r-2\right)+3\left(2r+5\right).

$$\frac{20r-8+6r+15}{\left(5r-2\right)\left(2r+5\right)}$$

Whakakotahitia ngā kupu rite i 20r-8+6r+15.

$$\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)}$$

Whakarohaina te \left(5r-2\right)\left(2r+5\right).

$$\frac{26r+7}{10r^{2}+21r-10}$$

Kimi Pārōnaki e ai ki r

$$-\frac{260r^{2}+140r+407}{\left(\left(5r-2\right)\left(2r+5\right)\right)^{2}}$$

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 2r+5 me 5r-2 ko \left(5r-2\right)\left(2r+5\right). Whakareatia \frac{4}{2r+5} ki te \frac{5r-2}{5r-2}. Whakareatia \frac{3}{5r-2} ki te \frac{2r+5}{2r+5}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)}+\frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)})$$

Tā te mea he rite te tauraro o \frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)} me \frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4\left(5r-2\right)+3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)})$$

Mahia ngā whakarea i roto o 4\left(5r-2\right)+3\left(2r+5\right).

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{20r-8+6r+15}{\left(5r-2\right)\left(2r+5\right)})$$

Whakakotahitia ngā kupu rite i 20r-8+6r+15.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 5r-2 ki ia tau o 2r+5.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{10r^{2}+25r-4r-10})$$

Pahekotia te 25r me -4r, ka 21r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{10r^{2}+21r-10})$$

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.

$$\frac{\left(10r^{2}+21r^{1}-10\right)\frac{\mathrm{d}}{\mathrm{d}r}(26r^{1}+7)-\left(26r^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}r}(10r^{2}+21r^{1}-10)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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}.

$$\frac{\left(10r^{2}+21r^{1}-10\right)\times 26r^{1-1}-\left(26r^{1}+7\right)\left(2\times 10r^{2-1}+21r^{1-1}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(10r^{2}+21r^{1}-10\right)\times 26r^{0}-\left(26r^{1}+7\right)\left(20r^{1}+21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Whakareatia 10r^{2}+21r^{1}-10 ki te 26r^{0}.

$$\frac{10r^{2}\times 26r^{0}+21r^{1}\times 26r^{0}-10\times 26r^{0}-\left(26r^{1}+7\right)\left(20r^{1}+21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Whakareatia 26r^{1}+7 ki te 20r^{1}+21r^{0}.

$$\frac{10r^{2}\times 26r^{0}+21r^{1}\times 26r^{0}-10\times 26r^{0}-\left(26r^{1}\times 20r^{1}+26r^{1}\times 21r^{0}+7\times 20r^{1}+7\times 21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{10\times 26r^{2}+21\times 26r^{1}-10\times 26r^{0}-\left(26\times 20r^{1+1}+26\times 21r^{1}+7\times 20r^{1}+7\times 21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Whakarūnātia.

$$\frac{260r^{2}+546r^{1}-260r^{0}-\left(520r^{2}+546r^{1}+140r^{1}+147r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-260r^{2}-140r^{1}-407r^{0}}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-260r^{2}-140r-407r^{0}}{\left(10r^{2}+21r-10\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-260r^{2}-140r-407}{\left(10r^{2}+21r-10\right)^{2}}$$