Issolvi 3x^{2}+5x+7+2x^3+3x+16/x^2+x=10x^3+12x+4/x-2+7x^3/x+1

$$3 x ^ { 2 } + 5 x + 7 + \frac { 2 x ^ { 3 } + 3 x + 16 } { x ^ { 2 } + x } = \frac { 10 x ^ { 3 } + 12 x + 4 } { x } - \frac { 2 + 7 x ^ { 3 } } { x + 1 }$$

Solvi għal x

$$x=3$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -1,0 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x\left(x+1\right), l-inqas denominatur komuni ta' x^{2}+x,x,x+1.

$$3x^{2}x\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 2 u 1 biex tikseb 3.

$$3x^{3}\left(x+1\right)+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

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

$$3x^{4}+3x^{3}+5xx\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

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

$$3x^{4}+3x^{3}+5x^{2}\left(x+1\right)+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 5x^{2} b'x+1.

$$3x^{4}+3x^{3}+5x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Ikkombina 3x^{3} u 5x^{3} biex tikseb 8x^{3}.

$$3x^{4}+8x^{3}+5x^{2}+x\left(x+1\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

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

$$3x^{4}+8x^{3}+5x^{2}+\left(x^{2}+x\right)\times 7+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+x b'7.

$$3x^{4}+8x^{3}+5x^{2}+7x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Ikkombina 5x^{2} u 7x^{2} biex tikseb 12x^{2}.

$$3x^{4}+8x^{3}+12x^{2}+7x+2x^{3}+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Ikkombina 8x^{3} u 2x^{3} biex tikseb 10x^{3}.

$$3x^{4}+10x^{3}+12x^{2}+7x+3x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Ikkombina 7x u 3x biex tikseb 10x.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=\left(x+1\right)\left(10x^{3}+12x+4\right)-x\left(2+7x^{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika x+1 b'10x^{3}+12x+4 u kkombina termini simili.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-x\left(2+7x^{3}\right)$$

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

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-\left(2x+7x^{4}\right)$$

Biex issib l-oppost ta' 2x+7x^{4}, sib l-oppost ta' kull terminu.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+16x+10x^{3}+4-2x-7x^{4}$$

Ikkombina 16x u -2x biex tikseb 14x.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=10x^{4}+12x^{2}+14x+10x^{3}+4-7x^{4}$$

Ikkombina 10x^{4} u -7x^{4} biex tikseb 3x^{4}.

$$3x^{4}+10x^{3}+12x^{2}+10x+16=3x^{4}+12x^{2}+14x+10x^{3}+4$$

Naqqas 3x^{4} miż-żewġ naħat.

$$3x^{4}+10x^{3}+12x^{2}+10x+16-3x^{4}=12x^{2}+14x+10x^{3}+4$$

Ikkombina 3x^{4} u -3x^{4} biex tikseb 0.

$$10x^{3}+12x^{2}+10x+16=12x^{2}+14x+10x^{3}+4$$

Naqqas 12x^{2} miż-żewġ naħat.

$$10x^{3}+12x^{2}+10x+16-12x^{2}=14x+10x^{3}+4$$

Ikkombina 12x^{2} u -12x^{2} biex tikseb 0.

$$10x^{3}+10x+16=14x+10x^{3}+4$$

Naqqas 14x miż-żewġ naħat.

$$10x^{3}+10x+16-14x=10x^{3}+4$$

Ikkombina 10x u -14x biex tikseb -4x.

$$10x^{3}-4x+16=10x^{3}+4$$

Naqqas 10x^{3} miż-żewġ naħat.

$$10x^{3}-4x+16-10x^{3}=4$$

Ikkombina 10x^{3} u -10x^{3} biex tikseb 0.

$$-4x+16=4$$

Naqqas 16 miż-żewġ naħat.

$$-4x=4-16$$

Naqqas 16 minn 4 biex tikseb -12.

$$-4x=-12$$

Iddividi ż-żewġ naħat b'-4.

$$x=\frac{-12}{-4}$$

Iddividi -12 b'-4 biex tikseb3.

$$x=3$$