Whakaoti i te x-4/x+7+1/3x-2=x-2/x+7

$$\frac { x - 4 } { x + 7 } + \frac { 1 } { 3 x - 2 } = \frac { x - 2 } { x + 7 }$$

Whakaoti mō x

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -7,\frac{2}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(3x-2\right)\left(x+7\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+7,3x-2.

$$\left(3x-2\right)\left(x-4\right)+x+7=\left(3x-2\right)\left(x-2\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-2 ki te x-4 ka whakakotahi i ngā kupu rite.

$$3x^{2}-14x+8+x+7=\left(3x-2\right)\left(x-2\right)$$

Pahekotia te -14x me x, ka -13x.

$$3x^{2}-13x+8+7=\left(3x-2\right)\left(x-2\right)$$

Tāpirihia te 8 ki te 7, ka 15.

$$3x^{2}-13x+15=\left(3x-2\right)\left(x-2\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-2 ki te x-2 ka whakakotahi i ngā kupu rite.

$$3x^{2}-13x+15=3x^{2}-8x+4$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$3x^{2}-13x+15-3x^{2}=-8x+4$$

Pahekotia te 3x^{2} me -3x^{2}, ka 0.

$$-13x+15=-8x+4$$

Me tāpiri te 8x ki ngā taha e rua.

$$-13x+15+8x=4$$

Pahekotia te -13x me 8x, ka -5x.

$$-5x+15=4$$

Tangohia te 15 mai i ngā taha e rua.

$$-5x=4-15$$

Tangohia te 15 i te 4, ka -11.

$$-5x=-11$$

Whakawehea ngā taha e rua ki te -5.

$$x=\frac{-11}{-5}$$

Ka taea te hautanga \frac{-11}{-5} te whakamāmā ki te \frac{11}{5} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{11}{5}$$