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

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

Whakaoti mō x

$$x=-\frac{83}{230}\approx -0.360869565$$

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.

$$12x^{2}+41x+35=\left(12x+3\right)\left(x-16\right)$$

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

$$12x^{2}+41x+35=12x^{2}-189x-48$$

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

$$12x^{2}+41x+35-12x^{2}=-189x-48$$

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

$$41x+35=-189x-48$$

Me tāpiri te 189x ki ngā taha e rua.

$$41x+35+189x=-48$$

Pahekotia te 41x me 189x, ka 230x.

$$230x+35=-48$$

Tangohia te 35 mai i ngā taha e rua.

$$230x=-48-35$$

Tangohia te 35 i te -48, ka -83.

$$230x=-83$$

Whakawehea ngā taha e rua ki te 230.

$$x=\frac{-83}{230}$$

Ka taea te hautanga \frac{-83}{230} te tuhi anō ko -\frac{83}{230} mā te tango i te tohu tōraro.

$$x=-\frac{83}{230}$$