Whakaoti i te (x-1)(x+2)-x(x+3)=(x-2)(x+2)-(x-1)^2

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

Whakaoti mō x

$$x=\frac{3}{4}=0.75$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+2 ka whakakotahi i ngā kupu rite.

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

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

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

Hei kimi i te tauaro o x^{2}+3x, kimihia te tauaro o ia taurangi.

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

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

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

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

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

Whakaarohia te \left(x-2\right)\left(x+2\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 2.

$$-2x-2=x^{2}-4-\left(x-1\right)^{2}$$

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

$$-2x-2=x^{2}-4-\left(x^{2}-2x+1\right)$$

Hei kimi i te tauaro o x^{2}-2x+1, kimihia te tauaro o ia taurangi.

$$-2x-2=x^{2}-4-x^{2}+2x-1$$

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

$$-2x-2=-4+2x-1$$

Tangohia te 1 i te -4, ka -5.

$$-2x-2=-5+2x$$

Tangohia te 2x mai i ngā taha e rua.

$$-2x-2-2x=-5$$

Pahekotia te -2x me -2x, ka -4x.

$$-4x-2=-5$$

Me tāpiri te 2 ki ngā taha e rua.

$$-4x=-5+2$$

Tāpirihia te -5 ki te 2, ka -3.

$$-4x=-3$$

Whakawehea ngā taha e rua ki te -4.

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

Ka taea te hautanga \frac{-3}{-4} te whakamāmā ki te \frac{3}{4} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{3}{4}$$