Whakaoti i te 1/sqrt{x}+1/-x9=1/20

$$\frac{ 1 }{ \sqrt{ x } } + \frac{ 1 }{ -x9 } = \frac{ 1 }{ 20 }$$

Whakaoti mō x_9

$$x_{9}=-\frac{20\sqrt{x}\left(\sqrt{x}+20\right)}{x-400}$$

$$x\neq 400\text{ and }x>0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \frac{1}{\sqrt{x}} mai i ngā taha e rua.

$$\frac{1}{-x_{9}}=\frac{1}{20}-\frac{1}{\sqrt{x}}$$

Tē taea kia ōrite te tāupe x_{9} ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20x_{9}, arā, te tauraro pātahi he tino iti rawa te kitea o -x_{9},20.

$$-20=20x_{9}\times \frac{1}{20}-20x_{9}x^{-\frac{1}{2}}$$

Whakareatia te 20 ki te \frac{1}{20}, ka 1.

$$-20=x_{9}-20x_{9}x^{-\frac{1}{2}}$$

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

$$x_{9}-20x_{9}x^{-\frac{1}{2}}=-20$$

Pahekotia ngā kīanga tau katoa e whai ana i te x_{9}.

$$\left(1-20x^{-\frac{1}{2}}\right)x_{9}=-20$$

He hanga arowhānui tō te whārite.

$$\left(1-\frac{20}{\sqrt{x}}\right)x_{9}=-20$$

Whakawehea ngā taha e rua ki te 1-20x^{-\frac{1}{2}}.

$$\frac{\left(1-\frac{20}{\sqrt{x}}\right)x_{9}}{1-\frac{20}{\sqrt{x}}}=-\frac{20}{1-\frac{20}{\sqrt{x}}}$$

Mā te whakawehe ki te 1-20x^{-\frac{1}{2}} ka wetekia te whakareanga ki te 1-20x^{-\frac{1}{2}}.

$$x_{9}=-\frac{20}{1-\frac{20}{\sqrt{x}}}$$

Whakawehe -20 ki te 1-20x^{-\frac{1}{2}}.

$$x_{9}=-\frac{20\sqrt{x}}{\sqrt{x}-20}$$

Tē taea kia ōrite te tāupe x_{9} ki 0.

$$x_{9}=-\frac{20\sqrt{x}}{\sqrt{x}-20}\text{, }x_{9}\neq 0$$

Whakaoti mō x

$$x=400\times \left(\frac{x_{9}}{x_{9}+20}\right)^{2}$$

$$x_{9}<-20\text{ or }x_{9}>0$$