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

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

Rešitev za x

$$x=3$$

Koraki za reševanje linearnih enačb

Spremenljivka x ne more biti enaka nobeni od vrednosti -1,0, ker deljenje z vrednostjo nič ni določeno. Pomnožite obe strani enačbe z x\left(x+1\right), najmanjšim skupnim mnogokratnikom števila x^{2}+x,x,x+1.

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

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 2 in 1, da dobite 3.

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

Uporabite distributivnost, da pomnožite 3x^{3} s/z x+1.

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

Pomnožite x in x, da dobite x^{2}.

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

Uporabite distributivnost, da pomnožite 5x^{2} s/z x+1.

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

Združite 3x^{3} in 5x^{3}, da dobite 8x^{3}.

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

Uporabite distributivnost, da pomnožite x s/z x+1.

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

Uporabite distributivnost, da pomnožite x^{2}+x s/z 7.

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

Združite 5x^{2} in 7x^{2}, da dobite 12x^{2}.

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

Združite 8x^{3} in 2x^{3}, da dobite 10x^{3}.

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

Združite 7x in 3x, da dobite 10x.

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

Uporabite lastnost distributivnosti za množenje x+1 krat 10x^{3}+12x+4 in kombiniranje pogojev podobnosti.

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

Uporabite distributivnost, da pomnožite x s/z 2+7x^{3}.

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

Če želite poiskati nasprotno vrednost za 2x+7x^{4}, poiščite nasprotno vrednost vsakega izraza.

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

Združite 16x in -2x, da dobite 14x.

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

Združite 10x^{4} in -7x^{4}, da dobite 3x^{4}.

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

Odštejte 3x^{4} na obeh straneh.

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

Združite 3x^{4} in -3x^{4}, da dobite 0.

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

Odštejte 12x^{2} na obeh straneh.

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

Združite 12x^{2} in -12x^{2}, da dobite 0.

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

Odštejte 14x na obeh straneh.

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

Združite 10x in -14x, da dobite -4x.

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

Odštejte 10x^{3} na obeh straneh.

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

Združite 10x^{3} in -10x^{3}, da dobite 0.

$$-4x+16=4$$

Odštejte 16 na obeh straneh.

$$-4x=4-16$$

Odštejte 16 od 4, da dobite -12.

$$-4x=-12$$

Delite obe strani z vrednostjo -4.

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

Delite -12 s/z -4, da dobite 3.

$$x=3$$