Issolvi 3/x+(6x+5)-6x+1/3x-1=3x+9x+6/3x-1+3x^2+1/x

$$\frac { 3 } { x } + ( 6 x + 5 ) - \frac { 6 x + 1 } { 3 x - 1 } = 3 x + \frac { 9 x + 6 } { 3 x - 1 } + \frac { 3 x ^ { 2 } + 1 } { x }$$

Solvi għal x

$$x=-\frac{1}{3}\approx -0.333333333$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri 0,\frac{1}{3} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x\left(3x-1\right), l-inqas denominatur komuni ta' x,3x-1.

$$\left(3x-1\right)\times 3+6xx\left(3x-1\right)+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 3x-1 b'3.

$$9x-3+6xx\left(3x-1\right)+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Immultiplika x u x biex tikseb x^{2}.

$$9x-3+6x^{2}\left(3x-1\right)+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 6x^{2} b'3x-1.

$$9x-3+18x^{3}-6x^{2}+x\left(3x-1\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x b'3x-1.

$$9x-3+18x^{3}-6x^{2}+\left(3x^{2}-x\right)\times 5-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 3x^{2}-x b'5.

$$9x-3+18x^{3}-6x^{2}+15x^{2}-5x-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Ikkombina -6x^{2} u 15x^{2} biex tikseb 9x^{2}.

$$9x-3+18x^{3}+9x^{2}-5x-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Ikkombina 9x u -5x biex tikseb 4x.

$$4x-3+18x^{3}+9x^{2}-x\left(6x+1\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x b'6x+1.

$$4x-3+18x^{3}+9x^{2}-\left(6x^{2}+x\right)=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Biex issib l-oppost ta' 6x^{2}+x, sib l-oppost ta' kull terminu.

$$4x-3+18x^{3}+9x^{2}-6x^{2}-x=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Ikkombina 9x^{2} u -6x^{2} biex tikseb 3x^{2}.

$$4x-3+18x^{3}+3x^{2}-x=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Ikkombina 4x u -x biex tikseb 3x.

$$3x-3+18x^{3}+3x^{2}=3xx\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Immultiplika x u x biex tikseb x^{2}.

$$3x-3+18x^{3}+3x^{2}=3x^{2}\left(3x-1\right)+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 3x^{2} b'3x-1.

$$3x-3+18x^{3}+3x^{2}=9x^{3}-3x^{2}+x\left(9x+6\right)+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x b'9x+6.

$$3x-3+18x^{3}+3x^{2}=9x^{3}-3x^{2}+9x^{2}+6x+\left(3x-1\right)\left(3x^{2}+1\right)$$

Ikkombina -3x^{2} u 9x^{2} biex tikseb 6x^{2}.

$$3x-3+18x^{3}+3x^{2}=9x^{3}+6x^{2}+6x+\left(3x-1\right)\left(3x^{2}+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 3x-1 b'3x^{2}+1.

$$3x-3+18x^{3}+3x^{2}=9x^{3}+6x^{2}+6x+9x^{3}+3x-3x^{2}-1$$

Ikkombina 9x^{3} u 9x^{3} biex tikseb 18x^{3}.

$$3x-3+18x^{3}+3x^{2}=18x^{3}+6x^{2}+6x+3x-3x^{2}-1$$

Ikkombina 6x u 3x biex tikseb 9x.

$$3x-3+18x^{3}+3x^{2}=18x^{3}+6x^{2}+9x-3x^{2}-1$$

Ikkombina 6x^{2} u -3x^{2} biex tikseb 3x^{2}.

$$3x-3+18x^{3}+3x^{2}=18x^{3}+3x^{2}+9x-1$$

Naqqas 18x^{3} miż-żewġ naħat.

$$3x-3+18x^{3}+3x^{2}-18x^{3}=3x^{2}+9x-1$$

Ikkombina 18x^{3} u -18x^{3} biex tikseb 0.

$$3x-3+3x^{2}=3x^{2}+9x-1$$

Naqqas 3x^{2} miż-żewġ naħat.

$$3x-3+3x^{2}-3x^{2}=9x-1$$

Ikkombina 3x^{2} u -3x^{2} biex tikseb 0.

$$3x-3=9x-1$$

Naqqas 9x miż-żewġ naħat.

$$3x-3-9x=-1$$

Ikkombina 3x u -9x biex tikseb -6x.

$$-6x-3=-1$$

Żid 3 maż-żewġ naħat.

$$-6x=-1+3$$

Żid -1 u 3 biex tikseb 2.

$$-6x=2$$

Iddividi ż-żewġ naħat b'-6.

$$x=\frac{2}{-6}$$

Naqqas il-frazzjoni \frac{2}{-6} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x=-\frac{1}{3}$$