Whakaoti i te 4/k+1+5/k=3/k

$$\frac { 4 } { k + 1 } + \frac { 5 } { k } = \frac { 3 } { k }$$

Whakaoti mō k

$$k=-\frac{1}{3}\approx -0.333333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe k ki tētahi o ngā uara -1,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te k\left(k+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o k+1,k.

$$k\times 4+\left(k+1\right)\times 5=\left(k+1\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te k+1 ki te 5.

$$k\times 4+5k+5=\left(k+1\right)\times 3$$

Pahekotia te k\times 4 me 5k, ka 9k.

$$9k+5=\left(k+1\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te k+1 ki te 3.

$$9k+5=3k+3$$

Tangohia te 3k mai i ngā taha e rua.

$$9k+5-3k=3$$

Pahekotia te 9k me -3k, ka 6k.

$$6k+5=3$$

Tangohia te 5 mai i ngā taha e rua.

$$6k=3-5$$

Tangohia te 5 i te 3, ka -2.

$$6k=-2$$

Whakawehea ngā taha e rua ki te 6.

$$k=\frac{-2}{6}$$

Whakahekea te hautanga \frac{-2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$k=-\frac{1}{3}$$