Whakaoti i te 01=2y(1-01/1+01-x/sqrt{996*10^6})-1

$$01=2y( \frac{ 1-01 }{ 1+01 } - \frac{ x }{ \sqrt{ 996 \times { 10 }^{ 6 } } } )-1$$

Whakaoti mō x

$$x=\frac{1000\sqrt{249}\left(2y-1\right)}{y}$$

$$y\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 0 ki te 1, ka 0.

$$0=2y\left(\frac{1-0\times 1}{1+0\times 1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Whakareatia te 0 ki te 1, ka 0.

$$0=2y\left(\frac{1-0}{1+0\times 1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Tangohia te 0 i te 1, ka 1.

$$0=2y\left(\frac{1}{1+0\times 1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Whakareatia te 0 ki te 1, ka 0.

$$0=2y\left(\frac{1}{1+0}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Tāpirihia te 1 ki te 0, ka 1.

$$0=2y\left(\frac{1}{1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$0=2y\left(1-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Tātaihia te 10 mā te pū o 6, kia riro ko 1000000.

$$0=2y\left(1-\frac{x}{\sqrt{996\times 1000000}}\right)-1$$

Whakareatia te 996 ki te 1000000, ka 996000000.

$$0=2y\left(1-\frac{x}{\sqrt{996000000}}\right)-1$$

Tauwehea te 996000000=2000^{2}\times 249. Tuhia anō te pūtake rua o te hua \sqrt{2000^{2}\times 249} hei hua o ngā pūtake rua \sqrt{2000^{2}}\sqrt{249}. Tuhia te pūtakerua o te 2000^{2}.

$$0=2y\left(1-\frac{x}{2000\sqrt{249}}\right)-1$$

Whakangāwaritia te tauraro o \frac{x}{2000\sqrt{249}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{249}.

$$0=2y\left(1-\frac{x\sqrt{249}}{2000\left(\sqrt{249}\right)^{2}}\right)-1$$

Ko te pūrua o \sqrt{249} ko 249.

$$0=2y\left(1-\frac{x\sqrt{249}}{2000\times 249}\right)-1$$

Whakareatia te 2000 ki te 249, ka 498000.

$$0=2y\left(1-\frac{x\sqrt{249}}{498000}\right)-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y ki te 1-\frac{x\sqrt{249}}{498000}.

$$0=2y+2y\left(-\frac{x\sqrt{249}}{498000}\right)-1$$

Whakakorea atu te tauwehe pūnoa nui rawa 498000 i roto i te 2 me te 498000.

$$0=2y+\frac{x\sqrt{249}}{-249000}y-1$$

Tuhia te \frac{x\sqrt{249}}{-249000}y hei hautanga kotahi.

$$0=2y+\frac{x\sqrt{249}y}{-249000}-1$$

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

$$2y+\frac{x\sqrt{249}y}{-249000}-1=0$$

Tangohia te 2y mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$\frac{x\sqrt{249}y}{-249000}-1=-2y$$

Me tāpiri te 1 ki ngā taha e rua.

$$\frac{x\sqrt{249}y}{-249000}=-2y+1$$

Whakareatia ngā taha e rua o te whārite ki te -249000.

$$x\sqrt{249}y=498000y-249000$$

He hanga arowhānui tō te whārite.

$$\sqrt{249}yx=498000y-249000$$

Whakawehea ngā taha e rua ki te \sqrt{249}y.

$$\frac{\sqrt{249}yx}{\sqrt{249}y}=\frac{498000y-249000}{\sqrt{249}y}$$

Mā te whakawehe ki te \sqrt{249}y ka wetekia te whakareanga ki te \sqrt{249}y.

$$x=\frac{498000y-249000}{\sqrt{249}y}$$

Whakawehe 498000y-249000 ki te \sqrt{249}y.

$$x=\frac{1000\sqrt{249}\left(2y-1\right)}{y}$$

Whakaoti mō y

$$y=\frac{249000}{-\sqrt{249}x+498000}$$

$$x\neq 2000\sqrt{249}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 0 ki te 1, ka 0.

$$0=2y\left(\frac{1-0\times 1}{1+0\times 1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Whakareatia te 0 ki te 1, ka 0.

$$0=2y\left(\frac{1-0}{1+0\times 1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Tangohia te 0 i te 1, ka 1.

$$0=2y\left(\frac{1}{1+0\times 1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Whakareatia te 0 ki te 1, ka 0.

$$0=2y\left(\frac{1}{1+0}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Tāpirihia te 1 ki te 0, ka 1.

$$0=2y\left(\frac{1}{1}-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$0=2y\left(1-\frac{x}{\sqrt{996\times 10^{6}}}\right)-1$$

Tātaihia te 10 mā te pū o 6, kia riro ko 1000000.

$$0=2y\left(1-\frac{x}{\sqrt{996\times 1000000}}\right)-1$$

Whakareatia te 996 ki te 1000000, ka 996000000.

$$0=2y\left(1-\frac{x}{\sqrt{996000000}}\right)-1$$

Tauwehea te 996000000=2000^{2}\times 249. Tuhia anō te pūtake rua o te hua \sqrt{2000^{2}\times 249} hei hua o ngā pūtake rua \sqrt{2000^{2}}\sqrt{249}. Tuhia te pūtakerua o te 2000^{2}.

$$0=2y\left(1-\frac{x}{2000\sqrt{249}}\right)-1$$

Whakangāwaritia te tauraro o \frac{x}{2000\sqrt{249}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{249}.

$$0=2y\left(1-\frac{x\sqrt{249}}{2000\left(\sqrt{249}\right)^{2}}\right)-1$$

Ko te pūrua o \sqrt{249} ko 249.

$$0=2y\left(1-\frac{x\sqrt{249}}{2000\times 249}\right)-1$$

Whakareatia te 2000 ki te 249, ka 498000.

$$0=2y\left(1-\frac{x\sqrt{249}}{498000}\right)-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y ki te 1-\frac{x\sqrt{249}}{498000}.

$$0=2y+2y\left(-\frac{x\sqrt{249}}{498000}\right)-1$$

Whakakorea atu te tauwehe pūnoa nui rawa 498000 i roto i te 2 me te 498000.

$$0=2y+\frac{x\sqrt{249}}{-249000}y-1$$

Tuhia te \frac{x\sqrt{249}}{-249000}y hei hautanga kotahi.

$$0=2y+\frac{x\sqrt{249}y}{-249000}-1$$

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

$$2y+\frac{x\sqrt{249}y}{-249000}-1=0$$

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2y+\frac{x\sqrt{249}y}{-249000}=1$$

Whakareatia ngā taha e rua o te whārite ki te -249000.

$$-498000y+x\sqrt{249}y=-249000$$

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

$$\left(-498000+x\sqrt{249}\right)y=-249000$$

He hanga arowhānui tō te whārite.

$$\left(\sqrt{249}x-498000\right)y=-249000$$

Whakawehea ngā taha e rua ki te -498000+x\sqrt{249}.

$$\frac{\left(\sqrt{249}x-498000\right)y}{\sqrt{249}x-498000}=-\frac{249000}{\sqrt{249}x-498000}$$

Mā te whakawehe ki te -498000+x\sqrt{249} ka wetekia te whakareanga ki te -498000+x\sqrt{249}.

$$y=-\frac{249000}{\sqrt{249}x-498000}$$