Whakaoti i te 4x-7/12x+3=x-16/3x+5

$$\frac { 4 x - 7 } { 12 x + 3 } = \frac { x - 16 } { 3 x + 5 }$$

Whakaoti mō x

$$x=-\frac{13}{188}\approx -0.069148936$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{5}{3},-\frac{1}{4} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3\left(3x+5\right)\left(4x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 12x+3,3x+5.

$$\left(3x+5\right)\left(4x-7\right)=\left(12x+3\right)\left(x-16\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+5 ki te 4x-7 ka whakakotahi i ngā kupu rite.

$$12x^{2}-x-35=\left(12x+3\right)\left(x-16\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 12x+3 ki te x-16 ka whakakotahi i ngā kupu rite.

$$12x^{2}-x-35=12x^{2}-189x-48$$

Tangohia te 12x^{2} mai i ngā taha e rua.

$$12x^{2}-x-35-12x^{2}=-189x-48$$

Pahekotia te 12x^{2} me -12x^{2}, ka 0.

$$-x-35=-189x-48$$

Me tāpiri te 189x ki ngā taha e rua.

$$-x-35+189x=-48$$

Pahekotia te -x me 189x, ka 188x.

$$188x-35=-48$$

Me tāpiri te 35 ki ngā taha e rua.

$$188x=-48+35$$

Tāpirihia te -48 ki te 35, ka -13.

$$188x=-13$$

Whakawehea ngā taha e rua ki te 188.

$$x=\frac{-13}{188}$$

Ka taea te hautanga \frac{-13}{188} te tuhi anō ko -\frac{13}{188} mā te tango i te tohu tōraro.

$$x=-\frac{13}{188}$$