Issolvi frac{24x(x^{3}+1)^{3/2}-3x^{2}(72x^{2}(x^3+1)^7/2)}{16(x^3+1)^3/2}

$$\frac { 24 x ( x ^ { 3 } + 1 ) ^ { 3 / 2 } - 3 x ^ { 2 } ( 72 x ^ { 2 } ( x ^ { 3 } + 1 ) ^ { 7 / 2 } ) } { 16 ( x ^ { 3 } + 1 ) ^ { 3 / 2 } }$$

Evalwa

$$-\frac{27x^{10}}{2}-27x^{7}-\frac{27x^{4}}{2}+\frac{3x}{2}$$

Passi Qosra tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 2 u 2 biex tikseb 4.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 72\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Immultiplika 3 u 72 biex tikseb 216.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Annulla 8\left(x^{3}+1\right)^{\frac{3}{2}} fin-numeratur u d-denominatur.

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

Espandi l-espressjoni.

$$\frac{-27x^{10}-54x^{7}-27x^{4}+3x}{2}$$

Fattur

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

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 2 u 2 biex tikseb 4.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 72\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Immultiplika 3 u 72 biex tikseb 216.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-216x^{4}\left(x^{3}+1\right)^{\frac{7}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}\left(-9x^{9}-18x^{6}-9x^{3}+1\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Annulla 8\left(x^{3}+1\right)^{\frac{3}{2}} fin-numeratur u d-denominatur.

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

Uża l-propjetà distributtiva biex timmultiplika 3x b'-9x^{9}-18x^{6}-9x^{3}+1.

$$factor(\frac{-27x^{10}-54x^{7}-27x^{4}+3x}{2})$$

Ikkunsidra li -27x^{10}-54x^{7}-27x^{4}+3x. Iffattura 'l barra 3.

$$3\left(-9x^{10}-18x^{7}-9x^{4}+x\right)$$

Ikkunsidra li -9x^{10}-18x^{7}-9x^{4}+x. Iffattura 'l barra x.

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

Erġa' ikteb l-espressjoni ffatturata kompluta. Issimplifika. Polynomial -9x^{9}-18x^{6}-9x^{3}+1 mhux fatturat billi m'għandux għeruq razzjonali.

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