Whakaoti i te 1/x-5+9/x+9=10/x^2+4x-45

$$\frac { 1 } { x - 5 } + \frac { 9 } { x + 9 } = \frac { 10 } { x ^ { 2 } + 4 x - 45 }$$

Whakaoti mō x

$$x = \frac{23}{5} = 4\frac{3}{5} = 4.6$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -9,5 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x+9\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-5,x+9,x^{2}+4x-45.

$$x+9+\left(x-5\right)\times 9=10$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 9.

$$x+9+9x-45=10$$

Pahekotia te x me 9x, ka 10x.

$$10x+9-45=10$$

Tangohia te 45 i te 9, ka -36.

$$10x-36=10$$

Me tāpiri te 36 ki ngā taha e rua.

$$10x=10+36$$

Tāpirihia te 10 ki te 36, ka 46.

$$10x=46$$

Whakawehea ngā taha e rua ki te 10.

$$x=\frac{46}{10}$$

Whakahekea te hautanga \frac{46}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{23}{5}$$