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

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

Whakaoti mō x

$$x=\frac{2}{3}\approx 0.666666667$$

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 2\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2,x+3,2\left(x+3\right).

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

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

$$\left(2x+6\right)\times \frac{1}{2}-2\times 3=5+2\left(x+3\right)\left(-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+6 ki te \frac{1}{2}.

$$x+3-2\times 3=5+2\left(x+3\right)\left(-1\right)$$

Whakareatia te -2 ki te 3, ka -6.

$$x+3-6=5+2\left(x+3\right)\left(-1\right)$$

Tangohia te 6 i te 3, ka -3.

$$x-3=5+2\left(x+3\right)\left(-1\right)$$

Whakareatia te 2 ki te -1, ka -2.

$$x-3=5-2\left(x+3\right)$$

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

$$x-3=5-2x-6$$

Tangohia te 6 i te 5, ka -1.

$$x-3=-1-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$x-3+2x=-1$$

Pahekotia te x me 2x, ka 3x.

$$3x-3=-1$$

Me tāpiri te 3 ki ngā taha e rua.

$$3x=-1+3$$

Tāpirihia te -1 ki te 3, ka 2.

$$3x=2$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{2}{3}$$