Whakaoti i te (2x+3/2x-3-2x-3/2x+3):24/4x^2-9

$$( \frac { 2 x + 3 } { 2 x - 3 } - \frac { 2 x - 3 } { 2 x + 3 } ) : \frac { 24 } { 4 x ^ { 2 } - 9 }$$

Aromātai

$$x$$

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

$$\frac{\frac{\left(2x+3\right)\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}-\frac{\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

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

$$\frac{\frac{\left(2x+3\right)\left(2x+3\right)-\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

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

$$\frac{\frac{4x^{2}+6x+6x+9-4x^{2}+6x+6x-9}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

Whakakotahitia ngā kupu rite i 4x^{2}+6x+6x+9-4x^{2}+6x+6x-9.

$$\frac{\frac{24x}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

Whakawehe \frac{24x}{\left(2x-3\right)\left(2x+3\right)} ki te \frac{24}{4x^{2}-9} mā te whakarea \frac{24x}{\left(2x-3\right)\left(2x+3\right)} ki te tau huripoki o \frac{24}{4x^{2}-9}.

$$\frac{24x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)\times 24}$$

Me whakakore tahi te 24 i te taurunga me te tauraro.

$$\frac{x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea.

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

Me whakakore tahi te \left(2x-3\right)\left(2x+3\right) i te taurunga me te tauraro.

$$x$$

Kimi Pārōnaki e ai ki x

$$1$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2x-3 me 2x+3 ko \left(2x-3\right)\left(2x+3\right). Whakareatia \frac{2x+3}{2x-3} ki te \frac{2x+3}{2x+3}. Whakareatia \frac{2x-3}{2x+3} ki te \frac{2x-3}{2x-3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{\left(2x+3\right)\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}-\frac{\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{\left(2x+3\right)\left(2x+3\right)-\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{4x^{2}+6x+6x+9-4x^{2}+6x+6x-9}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

Whakakotahitia ngā kupu rite i 4x^{2}+6x+6x+9-4x^{2}+6x+6x-9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{24x}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

Whakawehe \frac{24x}{\left(2x-3\right)\left(2x+3\right)} ki te \frac{24}{4x^{2}-9} mā te whakarea \frac{24x}{\left(2x-3\right)\left(2x+3\right)} ki te tau huripoki o \frac{24}{4x^{2}-9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)\times 24})$$

Me whakakore tahi te 24 i te taurunga me te tauraro.

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

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)}.

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

Me whakakore tahi te \left(2x-3\right)\left(2x+3\right) i te taurunga me te tauraro.

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

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$x^{1-1}$$

Tango 1 mai i 1.

$$x^{0}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$1$$