Whakaoti i te x-4/x+3=x-3/x+1

$$\frac { x - 4 } { x + 3 } = \frac { x - 3 } { x + 1 }$$

Whakaoti mō x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,-1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x+1\right)\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+3,x+1.

$$\left(x+1\right)\left(x-4\right)=\left(x+3\right)\left(x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te x-4 ka whakakotahi i ngā kupu rite.

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

Whakaarohia te \left(x+3\right)\left(x-3\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 3.

$$x^{2}-3x-4=x^{2}-9$$

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

$$x^{2}-3x-4-x^{2}=-9$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-3x-4=-9$$

Me tāpiri te 4 ki ngā taha e rua.

$$-3x=-9+4$$

Tāpirihia te -9 ki te 4, ka -5.

$$-3x=-5$$

Whakawehea ngā taha e rua ki te -3.

$$x=\frac{-5}{-3}$$

Ka taea te hautanga \frac{-5}{-3} te whakamāmā ki te \frac{5}{3} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{5}{3}$$