Whakaoti i te 2/2a+3-1/3-2a

$$\frac { 2 } { 2 a + 3 } - \frac { 1 } { 3 - 2 a }$$

Aromātai

$$\frac{3\left(1-2a\right)}{9-4a^{2}}$$

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 2a+3 me 3-2a ko \left(-2a+3\right)\left(2a+3\right). Whakareatia \frac{2}{2a+3} ki te \frac{-2a+3}{-2a+3}. Whakareatia \frac{1}{3-2a} ki te \frac{2a+3}{2a+3}.

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

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

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

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

$$\frac{-4a+6-2a-3}{\left(-2a+3\right)\left(2a+3\right)}$$

Whakakotahitia ngā kupu rite i -4a+6-2a-3.

$$\frac{-6a+3}{\left(-2a+3\right)\left(2a+3\right)}$$

Whakarohaina te \left(-2a+3\right)\left(2a+3\right).

$$\frac{-6a+3}{-4a^{2}+9}$$

Kimi Pārōnaki e ai ki a

$$-\frac{6\left(4a^{2}-4a+9\right)}{\left(4a^{2}-9\right)^{2}}$$

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 2a+3 me 3-2a ko \left(-2a+3\right)\left(2a+3\right). Whakareatia \frac{2}{2a+3} ki te \frac{-2a+3}{-2a+3}. Whakareatia \frac{1}{3-2a} ki te \frac{2a+3}{2a+3}.

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-4a+6-2a-3}{\left(-2a+3\right)\left(2a+3\right)})$$

Whakakotahitia ngā kupu rite i -4a+6-2a-3.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -2a+3 ki ia tau o 2a+3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-6a+3}{-4a^{2}-6a+6a+9})$$

Pahekotia te -6a me 6a, ka 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-6a+3}{-4a^{2}+9})$$

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.

$$\frac{\left(-4a^{2}+9\right)\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{1}+3)-\left(-6a^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}a}(-4a^{2}+9)}{\left(-4a^{2}+9\right)^{2}}$$

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}.

$$\frac{\left(-4a^{2}+9\right)\left(-6\right)a^{1-1}-\left(-6a^{1}+3\right)\times 2\left(-4\right)a^{2-1}}{\left(-4a^{2}+9\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(-4a^{2}+9\right)\left(-6\right)a^{0}-\left(-6a^{1}+3\right)\left(-8\right)a^{1}}{\left(-4a^{2}+9\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{-4a^{2}\left(-6\right)a^{0}+9\left(-6\right)a^{0}-\left(-6a^{1}\left(-8\right)a^{1}+3\left(-8\right)a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

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

$$\frac{-4\left(-6\right)a^{2}+9\left(-6\right)a^{0}-\left(-6\left(-8\right)a^{1+1}+3\left(-8\right)a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{24a^{2}-54a^{0}-\left(48a^{2}-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{24a^{2}-54a^{0}-48a^{2}-\left(-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(24-48\right)a^{2}-54a^{0}-\left(-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Tango 48 mai i 24.

$$\frac{-24a^{2}-54a^{0}-\left(-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{-24a^{2}-54a^{0}-\left(-24a\right)}{\left(-4a^{2}+9\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{-24a^{2}-54-\left(-24a\right)}{\left(-4a^{2}+9\right)^{2}}$$