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

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

Aromātai

$$\frac{31-3x}{\left(x-5\right)\left(x+3\right)}$$

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

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

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

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

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

$$\frac{2x+6-5x+25}{\left(x-5\right)\left(x+3\right)}$$

Whakakotahitia ngā kupu rite i 2x+6-5x+25.

$$\frac{-3x+31}{\left(x-5\right)\left(x+3\right)}$$

Whakarohaina te \left(x-5\right)\left(x+3\right).

$$\frac{-3x+31}{x^{2}-2x-15}$$

Kimi Pārōnaki e ai ki x

$$\frac{3x^{2}-62x+107}{x^{4}-4x^{3}-26x^{2}+60x+225}$$

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+6-5x+25}{\left(x-5\right)\left(x+3\right)})$$

Whakakotahitia ngā kupu rite i 2x+6-5x+25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{\left(x-5\right)\left(x+3\right)})$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-5 ki ia tau o x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{x^{2}+3x-5x-15})$$

Pahekotia te 3x me -5x, ka -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{x^{2}-2x-15})$$

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.

$$\frac{\left(x^{2}-2x^{1}-15\right)\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{1}+31)-\left(-3x^{1}+31\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}-15)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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}.

$$\frac{\left(x^{2}-2x^{1}-15\right)\left(-3\right)x^{1-1}-\left(-3x^{1}+31\right)\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}-2x^{1}-15\right)\left(-3\right)x^{0}-\left(-3x^{1}+31\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Whakareatia x^{2}-2x^{1}-15 ki te -3x^{0}.

$$\frac{x^{2}\left(-3\right)x^{0}-2x^{1}\left(-3\right)x^{0}-15\left(-3\right)x^{0}-\left(-3x^{1}+31\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Whakareatia -3x^{1}+31 ki te 2x^{1}-2x^{0}.

$$\frac{x^{2}\left(-3\right)x^{0}-2x^{1}\left(-3\right)x^{0}-15\left(-3\right)x^{0}-\left(-3x^{1}\times 2x^{1}-3x^{1}\left(-2\right)x^{0}+31\times 2x^{1}+31\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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

$$\frac{-3x^{2}-2\left(-3\right)x^{1}-15\left(-3\right)x^{0}-\left(-3\times 2x^{1+1}-3\left(-2\right)x^{1}+31\times 2x^{1}+31\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Whakarūnātia.

$$\frac{-3x^{2}+6x^{1}+45x^{0}-\left(-6x^{2}+6x^{1}+62x^{1}-62x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{3x^{2}-62x^{1}+107x^{0}}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{3x^{2}-62x+107x^{0}}{\left(x^{2}-2x-15\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{3x^{2}-62x+107\times 1}{\left(x^{2}-2x-15\right)^{2}}$$

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

$$\frac{3x^{2}-62x+107}{\left(x^{2}-2x-15\right)^{2}}$$