Whakaoti i te frac{sqrt{2x+3}-sqrt{x}}{x^2+4x+3}=v/1

$$\frac { \sqrt { 2 x + 3 } - \sqrt { x } } { x ^ { 2 } + 4 x + 3 } = \frac { v } { 1 }$$

Whakaoti mō v

$$v=\frac{\sqrt{2x+3}-\sqrt{x}}{\left(x+1\right)\left(x+3\right)}$$

$$x\geq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \left(x+1\right)\left(x+3\right).

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

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te x+3 ka whakakotahi i ngā kupu rite.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+4x+3 ki te v.

$$\sqrt{2x+3}-\sqrt{x}=x^{2}v+4xv+3v$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}v+4xv+3v=\sqrt{2x+3}-\sqrt{x}$$

Pahekotia ngā kīanga tau katoa e whai ana i te v.

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

Whakawehea ngā taha e rua ki te x^{2}+4x+3.

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

Mā te whakawehe ki te x^{2}+4x+3 ka wetekia te whakareanga ki te x^{2}+4x+3.

$$v=\frac{\sqrt{2x+3}-\sqrt{x}}{x^{2}+4x+3}$$

Whakawehe \sqrt{2x+3}-\sqrt{x} ki te x^{2}+4x+3.

$$v=\frac{\sqrt{2x+3}-\sqrt{x}}{\left(x+1\right)\left(x+3\right)}$$