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

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

Whakaoti mō x

$$x = -\frac{19}{14} = -1\frac{5}{14} \approx -1.357142857$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{5}{4},-1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(x+1\right)\left(4x+5\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x+2,4x+5.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+5 ki te 1-4x ka whakakotahi i ngā kupu rite.

$$-16x-16x^{2}+5+2\left(x+1\right)\left(4x+5\right)\times 2=\left(2x+2\right)\times 3$$

Whakareatia te 2 ki te 2, ka 4.

$$-16x-16x^{2}+5+4\left(x+1\right)\left(4x+5\right)=\left(2x+2\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+1.

$$-16x-16x^{2}+5+\left(4x+4\right)\left(4x+5\right)=\left(2x+2\right)\times 3$$

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

$$-16x-16x^{2}+5+16x^{2}+36x+20=\left(2x+2\right)\times 3$$

Pahekotia te -16x^{2} me 16x^{2}, ka 0.

$$-16x+5+36x+20=\left(2x+2\right)\times 3$$

Pahekotia te -16x me 36x, ka 20x.

$$20x+5+20=\left(2x+2\right)\times 3$$

Tāpirihia te 5 ki te 20, ka 25.

$$20x+25=\left(2x+2\right)\times 3$$

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

$$20x+25=6x+6$$

Tangohia te 6x mai i ngā taha e rua.

$$20x+25-6x=6$$

Pahekotia te 20x me -6x, ka 14x.

$$14x+25=6$$

Tangohia te 25 mai i ngā taha e rua.

$$14x=6-25$$

Tangohia te 25 i te 6, ka -19.

$$14x=-19$$

Whakawehea ngā taha e rua ki te 14.

$$x=\frac{-19}{14}$$

Ka taea te hautanga \frac{-19}{14} te tuhi anō ko -\frac{19}{14} mā te tango i te tohu tōraro.

$$x=-\frac{19}{14}$$