Issolvi x+1/x-1+x+2/x-2=22x+30/11x-18

$$\frac { x + 1 } { x - 1 } + \frac { x + 2 } { x - 2 } = \frac { 22 x + 30 } { 11 x - 18 }$$

Solvi għal x

$$x=-6$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri 1,\frac{18}{11},2 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-2\right)\left(x-1\right)\left(11x-18\right), l-inqas denominatur komuni ta' x-1,x-2,11x-18.

$$\left(x-2\right)\left(11x-18\right)\left(x+1\right)+\left(x-1\right)\left(11x-18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Uża l-propjetà distributtiva biex timmultiplika x-2 b'11x-18 u kkombina termini simili.

$$\left(11x^{2}-40x+36\right)\left(x+1\right)+\left(x-1\right)\left(11x-18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Uża l-propjetà distributtiva biex timmultiplika 11x^{2}-40x+36 b'x+1 u kkombina termini simili.

$$11x^{3}-29x^{2}-4x+36+\left(x-1\right)\left(11x-18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Uża l-propjetà distributtiva biex timmultiplika x-1 b'11x-18 u kkombina termini simili.

$$11x^{3}-29x^{2}-4x+36+\left(11x^{2}-29x+18\right)\left(x+2\right)=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Uża l-propjetà distributtiva biex timmultiplika 11x^{2}-29x+18 b'x+2 u kkombina termini simili.

$$11x^{3}-29x^{2}-4x+36+11x^{3}-7x^{2}-40x+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Ikkombina 11x^{3} u 11x^{3} biex tikseb 22x^{3}.

$$22x^{3}-29x^{2}-4x+36-7x^{2}-40x+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Ikkombina -29x^{2} u -7x^{2} biex tikseb -36x^{2}.

$$22x^{3}-36x^{2}-4x+36-40x+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Ikkombina -4x u -40x biex tikseb -44x.

$$22x^{3}-36x^{2}-44x+36+36=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Żid 36 u 36 biex tikseb 72.

$$22x^{3}-36x^{2}-44x+72=\left(x-2\right)\left(x-1\right)\left(22x+30\right)$$

Uża l-propjetà distributtiva biex timmultiplika x-2 b'x-1 u kkombina termini simili.

$$22x^{3}-36x^{2}-44x+72=\left(x^{2}-3x+2\right)\left(22x+30\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}-3x+2 b'22x+30 u kkombina termini simili.

$$22x^{3}-36x^{2}-44x+72=22x^{3}-36x^{2}-46x+60$$

Naqqas 22x^{3} miż-żewġ naħat.

$$22x^{3}-36x^{2}-44x+72-22x^{3}=-36x^{2}-46x+60$$

Ikkombina 22x^{3} u -22x^{3} biex tikseb 0.

$$-36x^{2}-44x+72=-36x^{2}-46x+60$$

Żid 36x^{2} maż-żewġ naħat.

$$-36x^{2}-44x+72+36x^{2}=-46x+60$$

Ikkombina -36x^{2} u 36x^{2} biex tikseb 0.

$$-44x+72=-46x+60$$

Żid 46x maż-żewġ naħat.

$$-44x+72+46x=60$$

Ikkombina -44x u 46x biex tikseb 2x.

$$2x+72=60$$

Naqqas 72 miż-żewġ naħat.

$$2x=60-72$$

Naqqas 72 minn 60 biex tikseb -12.

$$2x=-12$$

Iddividi ż-żewġ naħat b'2.

$$x=\frac{-12}{2}$$

Iddividi -12 b'2 biex tikseb-6.

$$x=-6$$