Whakaoti i te 4/x^2+3xdiv8/x^2+5x+6

$$\frac { 4 } { x ^ { 2 } + 3 x } \div \frac { 8 } { x ^ { 2 } + 5 x + 6 }$$

Aromātai

$$\frac{1}{2}+\frac{1}{x}$$

Ngā Hipanga Rongoā Poto

Whakawehe \frac{4}{x^{2}+3x} ki te \frac{8}{x^{2}+5x+6} mā te whakarea \frac{4}{x^{2}+3x} ki te tau huripoki o \frac{8}{x^{2}+5x+6}.

$$\frac{4\left(x^{2}+5x+6\right)}{\left(x^{2}+3x\right)\times 8}$$

Me whakakore tahi te 4 i te taurunga me te tauraro.

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

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea.

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

Me whakakore tahi te x+3 i te taurunga me te tauraro.

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

Kimi Pārōnaki e ai ki x

$$-\frac{1}{x^{2}}$$

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Otinga

Whakawehe \frac{4}{x^{2}+3x} ki te \frac{8}{x^{2}+5x+6} mā te whakarea \frac{4}{x^{2}+3x} ki te tau huripoki o \frac{8}{x^{2}+5x+6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x^{2}+5x+6\right)}{\left(x^{2}+3x\right)\times 8})$$

Me whakakore tahi te 4 i te taurunga me te tauraro.

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

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{x^{2}+5x+6}{2\left(x^{2}+3x\right)}.

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

Me whakakore tahi te x+3 i te taurunga me te tauraro.

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

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

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

Tangohia ngā taiapa kāore i te hiahiatia.

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

Pahekotia ngā kīanga tau ōrite.

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

Tango 2 mai i 2.

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

Hei hiki i te hua o ngā tau e rua, neke atu rānei ki tētahi pū, hīkina ia tau ki te pū ka tuhi ko tāna hua.

$$-\frac{4x^{0}}{2^{2}x^{2}}$$

Hīkina te 2 ki te pū 2.

$$-\frac{4x^{0}}{4x^{2}}$$

Whakareatia 1 ki te 2.

$$\frac{-4x^{0}}{4x^{2}}$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

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

Mahia ngā tātaitanga.

$$-x^{-2}$$