Rešite frac{24x{left(x^3+1right)}^frac{3{2}}-3x^272x^2{left(x^3+1right)}^frac{1{2}}}{16{left({x}^3+1right)}^frac{3{2}}}

$$\frac{ 24x { \left( { x }^{ 3 } +1 \right) }^{ \frac{ 3 }{ 2 } } -3 { x }^{ 2 } 72 { x }^{ 2 } { \left( { x }^{ 3 } +1 \right) }^{ \frac{ 1 }{ 2 } } }{ 16 { \left( { x }^{ 3 } +1 \right) }^{ \frac{ 3 }{ 2 } } }$$

Ovrednoti

$$-\frac{3x\left(8x^{3}-1\right)}{2\left(x^{3}+1\right)}$$

Kratka navodila za rešitev

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 2 in 2, da dobite 4.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 72\left(x^{3}+1\right)^{\frac{1}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Pomnožite 3 in 72, da dobite 216.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{1}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{24x\left(2x-1\right)\sqrt{x^{3}+1}\left(-4x^{2}-2x-1\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Okrajšaj 8\sqrt{x^{3}+1} v števcu in imenovalcu.

$$\frac{3x\left(2x-1\right)\left(-4x^{2}-2x-1\right)}{2\left(x^{3}+1\right)}$$

Razširite izraz.

$$\frac{-24x^{4}+3x}{2x^{3}+2}$$

Faktoriziraj

$$-\frac{3x\left(2x-1\right)\left(4x^{2}+2x+1\right)}{2\left(x+1\right)\left(x^{2}-x+1\right)}$$