Whakaoti i te 2/x+4+3/x

$$\frac { 2 } { x + 4 } + \frac { 3 } { x }$$

Aromātai

$$\frac{5x+12}{x\left(x+4\right)}$$

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

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

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

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

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

$$\frac{2x+3x+12}{x\left(x+4\right)}$$

Whakakotahitia ngā kupu rite i 2x+3x+12.

$$\frac{5x+12}{x\left(x+4\right)}$$

Whakarohaina te x\left(x+4\right).

$$\frac{5x+12}{x^{2}+4x}$$

Kimi Pārōnaki e ai ki x

$$-\frac{5x^{2}+24x+48}{\left(x\left(x+4\right)\right)^{2}}$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{x\left(x+4\right)}+\frac{3\left(x+4\right)}{x\left(x+4\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+3\left(x+4\right)}{x\left(x+4\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+3x+12}{x\left(x+4\right)})$$

Whakakotahitia ngā kupu rite i 2x+3x+12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x+12}{x\left(x+4\right)})$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x+12}{x^{2}+4x})$$

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.

$$\frac{\left(x^{2}+4x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1}+12)-\left(5x^{1}+12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+4x^{1})}{\left(x^{2}+4x^{1}\right)^{2}}$$

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}.

$$\frac{\left(x^{2}+4x^{1}\right)\times 5x^{1-1}-\left(5x^{1}+12\right)\left(2x^{2-1}+4x^{1-1}\right)}{\left(x^{2}+4x^{1}\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(x^{2}+4x^{1}\right)\times 5x^{0}-\left(5x^{1}+12\right)\left(2x^{1}+4x^{0}\right)}{\left(x^{2}+4x^{1}\right)^{2}}$$

Whakareatia x^{2}+4x^{1} ki te 5x^{0}.

$$\frac{x^{2}\times 5x^{0}+4x^{1}\times 5x^{0}-\left(5x^{1}+12\right)\left(2x^{1}+4x^{0}\right)}{\left(x^{2}+4x^{1}\right)^{2}}$$

Whakareatia 5x^{1}+12 ki te 2x^{1}+4x^{0}.

$$\frac{x^{2}\times 5x^{0}+4x^{1}\times 5x^{0}-\left(5x^{1}\times 2x^{1}+5x^{1}\times 4x^{0}+12\times 2x^{1}+12\times 4x^{0}\right)}{\left(x^{2}+4x^{1}\right)^{2}}$$

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

$$\frac{5x^{2}+4\times 5x^{1}-\left(5\times 2x^{1+1}+5\times 4x^{1}+12\times 2x^{1}+12\times 4x^{0}\right)}{\left(x^{2}+4x^{1}\right)^{2}}$$

Whakarūnātia.

$$\frac{5x^{2}+20x^{1}-\left(10x^{2}+20x^{1}+24x^{1}+48x^{0}\right)}{\left(x^{2}+4x^{1}\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{-5x^{2}-24x^{1}-48x^{0}}{\left(x^{2}+4x^{1}\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-5x^{2}-24x-48x^{0}}{\left(x^{2}+4x\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-5x^{2}-24x-48}{\left(x^{2}+4x\right)^{2}}$$