Whakaoti i te {l}{7x+2/2x-3+5x+4/x=34x^2+43x-2/4x^2-9+10-x/2x^2-3x}{y=333}{z=y}{a=z}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { \frac{7 x + 2}{2 x - 3} + \frac{5 x + 4}{x} = \frac{34 x ^ {2} + 43 x - 2}{4 x ^ {2} - 9} + \frac{10 - x}{2 x ^ {2} - 3 x} }\\ { y = 333 }\\ { z = y }\\ { a = z }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Whakaoti mō x, y, z, a, b, c, d

$$d=333$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{3}{2},0,\frac{3}{2} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(2x-3\right)\left(2x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x-3,x,4x^{2}-9,2x^{2}-3x.

$$x\left(2x+3\right)\left(7x+2\right)+\left(4x^{2}-9\right)\left(5x+4\right)=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

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

$$\left(2x^{2}+3x\right)\left(7x+2\right)+\left(4x^{2}-9\right)\left(5x+4\right)=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x^{2}+3x ki te 7x+2 ka whakakotahi i ngā kupu rite.

$$14x^{3}+25x^{2}+6x+\left(4x^{2}-9\right)\left(5x+4\right)=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x^{2}-9 ki te 5x+4.

$$14x^{3}+25x^{2}+6x+20x^{3}+16x^{2}-45x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Pahekotia te 14x^{3} me 20x^{3}, ka 34x^{3}.

$$34x^{3}+25x^{2}+6x+16x^{2}-45x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Pahekotia te 25x^{2} me 16x^{2}, ka 41x^{2}.

$$34x^{3}+41x^{2}+6x-45x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Pahekotia te 6x me -45x, ka -39x.

$$34x^{3}+41x^{2}-39x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 34x^{2}+43x-2.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+43x^{2}-2x+\left(2x+3\right)\left(10-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+3 ki te 10-x ka whakakotahi i ngā kupu rite.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+43x^{2}-2x+17x-2x^{2}+30$$

Pahekotia te -2x me 17x, ka 15x.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+43x^{2}+15x-2x^{2}+30$$

Pahekotia te 43x^{2} me -2x^{2}, ka 41x^{2}.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+41x^{2}+15x+30$$

Tangohia te 34x^{3} mai i ngā taha e rua.

$$34x^{3}+41x^{2}-39x-36-34x^{3}=41x^{2}+15x+30$$

Pahekotia te 34x^{3} me -34x^{3}, ka 0.

$$41x^{2}-39x-36=41x^{2}+15x+30$$

Tangohia te 41x^{2} mai i ngā taha e rua.

$$41x^{2}-39x-36-41x^{2}=15x+30$$

Pahekotia te 41x^{2} me -41x^{2}, ka 0.

$$-39x-36=15x+30$$

Tangohia te 15x mai i ngā taha e rua.

$$-39x-36-15x=30$$

Pahekotia te -39x me -15x, ka -54x.

$$-54x-36=30$$

Me tāpiri te 36 ki ngā taha e rua.

$$-54x=30+36$$

Tāpirihia te 30 ki te 36, ka 66.

$$-54x=66$$

Whakawehea ngā taha e rua ki te -54.

$$x=\frac{66}{-54}$$

Whakahekea te hautanga \frac{66}{-54} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=-\frac{11}{9}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{11}{9} y=333 z=333 a=333 b=333 c=333 d=333$$