Whakaoti i te 3/x-2-2/x+3=1

$$\frac { 3 } { x - 2 } - \frac { 2 } { x + 3 } = 1$$

Whakaoti mō x

$$x=\sqrt{19}\approx 4.358898944$$

$$x=-\sqrt{19}\approx -4.358898944$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-2,x+3.

$$\left(x+3\right)\times 3-\left(x-2\right)\times 2=\left(x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+3 ki te 3.

$$3x+9-\left(x-2\right)\times 2=\left(x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 2.

$$3x+9-\left(2x-4\right)=\left(x-2\right)\left(x+3\right)$$

Hei kimi i te tauaro o 2x-4, kimihia te tauaro o ia taurangi.

$$3x+9-2x+4=\left(x-2\right)\left(x+3\right)$$

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

$$x+9+4=\left(x-2\right)\left(x+3\right)$$

Tāpirihia te 9 ki te 4, ka 13.

$$x+13=\left(x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x+13=x^{2}+x-6$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x+13-x^{2}=x-6$$

Tangohia te x mai i ngā taha e rua.

$$x+13-x^{2}-x=-6$$

Pahekotia te x me -x, ka 0.

$$13-x^{2}=-6$$

Tangohia te 13 mai i ngā taha e rua.

$$-x^{2}=-6-13$$

Tangohia te 13 i te -6, ka -19.

$$-x^{2}=-19$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=\frac{-19}{-1}$$

Ka taea te hautanga \frac{-19}{-1} te whakamāmā ki te 19 mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=19$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$x=\sqrt{19} x=-\sqrt{19}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-2,x+3.

$$\left(x+3\right)\times 3-\left(x-2\right)\times 2=\left(x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+3 ki te 3.

$$3x+9-\left(x-2\right)\times 2=\left(x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 2.

$$3x+9-\left(2x-4\right)=\left(x-2\right)\left(x+3\right)$$

Hei kimi i te tauaro o 2x-4, kimihia te tauaro o ia taurangi.

$$3x+9-2x+4=\left(x-2\right)\left(x+3\right)$$

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

$$x+9+4=\left(x-2\right)\left(x+3\right)$$

Tāpirihia te 9 ki te 4, ka 13.

$$x+13=\left(x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x+13=x^{2}+x-6$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x+13-x^{2}=x-6$$

Tangohia te x mai i ngā taha e rua.

$$x+13-x^{2}-x=-6$$

Pahekotia te x me -x, ka 0.

$$13-x^{2}=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$13-x^{2}+6=0$$

Tāpirihia te 13 ki te 6, ka 19.

$$19-x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-x^{2}+19=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me 19 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\times 19}}{2\left(-1\right)}$$

Whakareatia 4 ki te 19.

$$x=\frac{0±\sqrt{76}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 76.

$$x=\frac{0±2\sqrt{19}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±2\sqrt{19}}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{19}}{-2} ina he tāpiri te ±.

$$x=-\sqrt{19}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{19}}{-2} ina he tango te ±.

$$x=\sqrt{19}$$

Kua oti te whārite te whakatau.

$$x=-\sqrt{19} x=\sqrt{19}$$