Whakaoti i te y_{n}=2n-1/2n+1

$$y _ { n } = \frac { 2 n - 1 } { 2 n + 1 }$$

Whakaoti mō n

$$n=-\frac{y_{n}+1}{2\left(y_{n}-1\right)}$$

$$y_{n}\neq 1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe n ki -\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2n+1.

$$y_{n}\left(2n+1\right)=2n-1$$

Whakamahia te āhuatanga tohatoha hei whakarea te y_{n} ki te 2n+1.

$$2y_{n}n+y_{n}=2n-1$$

Tangohia te 2n mai i ngā taha e rua.

$$2y_{n}n+y_{n}-2n=-1$$

Tangohia te y_{n} mai i ngā taha e rua.

$$2y_{n}n-2n=-1-y_{n}$$

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

$$\left(2y_{n}-2\right)n=-1-y_{n}$$

He hanga arowhānui tō te whārite.

$$\left(2y_{n}-2\right)n=-y_{n}-1$$

Whakawehea ngā taha e rua ki te 2y_{n}-2.

$$\frac{\left(2y_{n}-2\right)n}{2y_{n}-2}=\frac{-y_{n}-1}{2y_{n}-2}$$

Mā te whakawehe ki te 2y_{n}-2 ka wetekia te whakareanga ki te 2y_{n}-2.

$$n=\frac{-y_{n}-1}{2y_{n}-2}$$

Whakawehe -1-y_{n} ki te 2y_{n}-2.

$$n=-\frac{y_{n}+1}{2\left(y_{n}-1\right)}$$

Tē taea kia ōrite te tāupe n ki -\frac{1}{2}.

$$n=-\frac{y_{n}+1}{2\left(y_{n}-1\right)}\text{, }n\neq -\frac{1}{2}$$

Whakaoti mō y_n

$$y_{n}=-\frac{1-2n}{2n+1}$$

$$n\neq -\frac{1}{2}$$