Whakaoti mō w (complex solution)
\left\{\begin{matrix}w=\left(\frac{x+1}{x-1}\right)^{2}y\text{, }&x\neq 1\text{ and }x\neq -1\\w\in \mathrm{C}\text{, }&x=1\text{ and }y=0\end{matrix}\right.
Whakaoti mō w
\left\{\begin{matrix}w=\left(\frac{x+1}{x-1}\right)^{2}y\text{, }&|x|\neq 1\\w\in \mathrm{R}\text{, }&x=1\text{ and }y=0\end{matrix}\right.
Whakaoti mō x (complex solution)
\left\{\begin{matrix}x=\frac{2\sqrt{wy}+w+y}{w-y}\text{; }x=\frac{-2\sqrt{wy}+w+y}{w-y}\text{, }&w\neq 0\text{ and }y\neq w\\x=0\text{, }&y=w\text{ and }w\neq 0\\x\neq -1\text{, }&y=0\text{ and }w=0\end{matrix}\right.
Whakaoti mō x
\left\{\begin{matrix}x=\frac{2\sqrt{wy}+w+y}{w-y}\text{; }x=\frac{-2\sqrt{wy}+w+y}{w-y}\text{, }&\left(y\neq w\text{ and }y\leq 0\text{ and }w<0\right)\text{ or }\left(y\neq w\text{ and }y\geq 0\text{ and }w>0\right)\\x=0\text{, }&y=w\text{ and }w\neq 0\\x\neq -1\text{, }&y=0\text{ and }w=0\end{matrix}\right.
Graph
Tohaina
Kua tāruatia ki te papatopenga
y=\frac{\left(x-1\right)^{2}}{\left(x+1\right)^{2}}w
Kia whakarewa i te \frac{x-1}{x+1} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.
y=\frac{\left(x-1\right)^{2}w}{\left(x+1\right)^{2}}
Tuhia te \frac{\left(x-1\right)^{2}}{\left(x+1\right)^{2}}w hei hautanga kotahi.
y=\frac{\left(x^{2}-2x+1\right)w}{\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}.
y=\frac{\left(x^{2}-2x+1\right)w}{x^{2}+2x+1}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.
\frac{\left(x^{2}-2x+1\right)w}{x^{2}+2x+1}=y
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
\frac{x^{2}w-2xw+w}{x^{2}+2x+1}=y
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-2x+1 ki te w.
x^{2}w-2xw+w=y\left(x+1\right)^{2}
Whakareatia ngā taha e rua o te whārite ki te \left(x+1\right)^{2}.
x^{2}w-2xw+w=y\left(x^{2}+2x+1\right)
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.
x^{2}w-2xw+w=yx^{2}+2yx+y
Whakamahia te āhuatanga tohatoha hei whakarea te y ki te x^{2}+2x+1.
\left(x^{2}-2x+1\right)w=yx^{2}+2yx+y
Pahekotia ngā kīanga tau katoa e whai ana i te w.
\left(x^{2}-2x+1\right)w=2xy+yx^{2}+y
He hanga arowhānui tō te whārite.
\frac{\left(x^{2}-2x+1\right)w}{x^{2}-2x+1}=\frac{y\left(x+1\right)^{2}}{x^{2}-2x+1}
Whakawehea ngā taha e rua ki te x^{2}-2x+1.
w=\frac{y\left(x+1\right)^{2}}{x^{2}-2x+1}
Mā te whakawehe ki te x^{2}-2x+1 ka wetekia te whakareanga ki te x^{2}-2x+1.
w=\frac{y\left(x+1\right)^{2}}{\left(x-1\right)^{2}}
Whakawehe y\left(1+x\right)^{2} ki te x^{2}-2x+1.
y=\frac{\left(x-1\right)^{2}}{\left(x+1\right)^{2}}w
Kia whakarewa i te \frac{x-1}{x+1} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.
y=\frac{\left(x-1\right)^{2}w}{\left(x+1\right)^{2}}
Tuhia te \frac{\left(x-1\right)^{2}}{\left(x+1\right)^{2}}w hei hautanga kotahi.
y=\frac{\left(x^{2}-2x+1\right)w}{\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}.
y=\frac{\left(x^{2}-2x+1\right)w}{x^{2}+2x+1}
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.
\frac{\left(x^{2}-2x+1\right)w}{x^{2}+2x+1}=y
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
\frac{x^{2}w-2xw+w}{x^{2}+2x+1}=y
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-2x+1 ki te w.
x^{2}w-2xw+w=y\left(x+1\right)^{2}
Whakareatia ngā taha e rua o te whārite ki te \left(x+1\right)^{2}.
x^{2}w-2xw+w=y\left(x^{2}+2x+1\right)
Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.
x^{2}w-2xw+w=yx^{2}+2yx+y
Whakamahia te āhuatanga tohatoha hei whakarea te y ki te x^{2}+2x+1.
\left(x^{2}-2x+1\right)w=yx^{2}+2yx+y
Pahekotia ngā kīanga tau katoa e whai ana i te w.
\left(x^{2}-2x+1\right)w=2xy+yx^{2}+y
He hanga arowhānui tō te whārite.
\frac{\left(x^{2}-2x+1\right)w}{x^{2}-2x+1}=\frac{y\left(x+1\right)^{2}}{x^{2}-2x+1}
Whakawehea ngā taha e rua ki te x^{2}-2x+1.
w=\frac{y\left(x+1\right)^{2}}{x^{2}-2x+1}
Mā te whakawehe ki te x^{2}-2x+1 ka wetekia te whakareanga ki te x^{2}-2x+1.
w=\frac{y\left(x+1\right)^{2}}{\left(x-1\right)^{2}}
Whakawehe y\left(1+x\right)^{2} ki te x^{2}-2x+1.
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