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

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

Whakaoti mō x

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,-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+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+2,x+1.

$$\left(x+1\right)\left(x+1\right)=\left(x+2\right)\left(x-3\right)$$

Whakareatia te x+1 ki te x+1, ka \left(x+1\right)^{2}.

$$\left(x+1\right)^{2}=\left(x+2\right)\left(x-3\right)$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$x^{2}+2x+1=\left(x+2\right)\left(x-3\right)$$

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

$$x^{2}+2x+1=x^{2}-x-6$$

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

$$x^{2}+2x+1-x^{2}=-x-6$$

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

$$2x+1=-x-6$$

Me tāpiri te x ki ngā taha e rua.

$$2x+1+x=-6$$

Pahekotia te 2x me x, ka 3x.

$$3x+1=-6$$

Tangohia te 1 mai i ngā taha e rua.

$$3x=-6-1$$

Tangohia te 1 i te -6, ka -7.

$$3x=-7$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{-7}{3}$$

Ka taea te hautanga \frac{-7}{3} te tuhi anō ko -\frac{7}{3} mā te tango i te tohu tōraro.

$$x=-\frac{7}{3}$$