Whakaoti i te 5(x-2)+6/3x=5x/11-3(2-x)

$$\frac { 5 ( x - 2 ) + 6 } { 3 x } = \frac { 5 x } { 11 - 3 ( 2 - x ) }$$

Whakaoti mō x

$$x = \frac{20}{13} = 1\frac{7}{13} \approx 1.538461538$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{5}{3},0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x\left(3x+5\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3x,11-3\left(2-x\right).

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x-2.

$$\left(3x+5\right)\left(5x-10+6\right)=3x\times 5x$$

Tāpirihia te -10 ki te 6, ka -4.

$$\left(3x+5\right)\left(5x-4\right)=3x\times 5x$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+5 ki te 5x-4 ka whakakotahi i ngā kupu rite.

$$15x^{2}+13x-20=3x\times 5x$$

Whakareatia te x ki te x, ka x^{2}.

$$15x^{2}+13x-20=3x^{2}\times 5$$

Whakareatia te 3 ki te 5, ka 15.

$$15x^{2}+13x-20=15x^{2}$$

Tangohia te 15x^{2} mai i ngā taha e rua.

$$15x^{2}+13x-20-15x^{2}=0$$

Pahekotia te 15x^{2} me -15x^{2}, ka 0.

$$13x-20=0$$

Me tāpiri te 20 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$13x=20$$

Whakawehea ngā taha e rua ki te 13.

$$x=\frac{20}{13}$$