Whakaoti i te 2x+5/x-3=1/3+4/x-3

$$\frac{ 2x+5 }{ x-3 } = \frac{ 1 }{ 3 } + \frac{ 4 }{ x-3 }$$

Whakaoti mō x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-3,3.

$$3\left(2x+5\right)=3\left(x-3\right)\times \frac{1}{3}+3\times 4$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 2x+5.

$$6x+15=3\left(x-3\right)\times \frac{1}{3}+3\times 4$$

Whakareatia te 3 ki te \frac{1}{3}, ka 1.

$$6x+15=x-3+3\times 4$$

Whakareatia te 3 ki te 4, ka 12.

$$6x+15=x-3+12$$

Tāpirihia te -3 ki te 12, ka 9.

$$6x+15=x+9$$

Tangohia te x mai i ngā taha e rua.

$$6x+15-x=9$$

Pahekotia te 6x me -x, ka 5x.

$$5x+15=9$$

Tangohia te 15 mai i ngā taha e rua.

$$5x=9-15$$

Tangohia te 15 i te 9, ka -6.

$$5x=-6$$

Whakawehea ngā taha e rua ki te 5.

$$x=\frac{-6}{5}$$

Ka taea te hautanga \frac{-6}{5} te tuhi anō ko -\frac{6}{5} mā te tango i te tohu tōraro.

$$x=-\frac{6}{5}$$