Issolvi {l}{7x+2/2x-3+5x+4/x=34x^2+43x-2/4x^2-9+10-x/2x^2-3x}{y=333}{text{Solvefor}ztext{where}}{z=y}

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

Solvi għal x, y, z

$$z=333$$

Passi tas-Soluzzjonijiet

Ikkunsidra l-ewwel ekwazzjoni. Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -\frac{3}{2},0,\frac{3}{2} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x\left(2x-3\right)\left(2x+3\right), l-inqas denominatur komuni ta' 2x-3,x,4x^{2}-9,2x^{2}-3x.

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

Uża l-propjetà distributtiva biex timmultiplika x b'2x+3.

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

Uża l-propjetà distributtiva biex timmultiplika 2x^{2}+3x b'7x+2 u kkombina termini simili.

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

Uża l-propjetà distributtiva biex timmultiplika 4x^{2}-9 b'5x+4.

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

Ikkombina 14x^{3} u 20x^{3} biex tikseb 34x^{3}.

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

Ikkombina 25x^{2} u 16x^{2} biex tikseb 41x^{2}.

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

Ikkombina 6x u -45x biex tikseb -39x.

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

Uża l-propjetà distributtiva biex timmultiplika x b'34x^{2}+43x-2.

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

Uża l-propjetà distributtiva biex timmultiplika 2x+3 b'10-x u kkombina termini simili.

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

Ikkombina -2x u 17x biex tikseb 15x.

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

Ikkombina 43x^{2} u -2x^{2} biex tikseb 41x^{2}.

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

Naqqas 34x^{3} miż-żewġ naħat.

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

Ikkombina 34x^{3} u -34x^{3} biex tikseb 0.

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

Naqqas 41x^{2} miż-żewġ naħat.

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

Ikkombina 41x^{2} u -41x^{2} biex tikseb 0.

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

Naqqas 15x miż-żewġ naħat.

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

Ikkombina -39x u -15x biex tikseb -54x.

$$-54x-36=30$$

Żid 36 maż-żewġ naħat.

$$-54x=30+36$$

Żid 30 u 36 biex tikseb 66.

$$-54x=66$$

Iddividi ż-żewġ naħat b'-54.

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

Naqqas il-frazzjoni \frac{66}{-54} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 6.

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

Is-sistema issa solvuta.

$$x=-\frac{11}{9} y=333 z=333$$