Issolvi frac{24x(x^{3}+1)^{3/2}-3x^{2}(12x^{2}x^{3}*(x^3+1)^3/2)}{16(x^3+1)^3/2}

$$\frac { 24 x ( x ^ { 3 } + 1 ) ^ { 3 / 2 } - 3 x ^ { 2 } ( 12 x ^ { 2 } x ^ { 3 } \cdot ( x ^ { 3 } + 1 ) ^ { 3 / 2 } ) } { 16 ( x ^ { 3 } + 1 ) ^ { 3 / 2 } }$$

Evalwa

$$-\frac{9x^{7}}{4}+\frac{3x}{2}$$

Passi Qosra tas-Soluzzjonijiet

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

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 12x^{3}\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 4 u 3 biex tikseb 7.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{7}\times 12\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Immultiplika 3 u 12 biex tikseb 36.

$$\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-36x^{7}\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

$$\frac{12x\left(x^{3}+1\right)^{\frac{3}{2}}\left(-3x^{6}+2\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}}$$

Annulla 4\left(x^{3}+1\right)^{\frac{3}{2}} fin-numeratur u d-denominatur.

$$\frac{3x\left(-3x^{6}+2\right)}{4}$$

Espandi l-espressjoni.

$$\frac{-9x^{7}+6x}{4}$$

Fattur

$$\frac{3x\left(2-3x^{6}\right)}{4}$$

Passi tas-Soluzzjonijiet

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

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{4}\times 12x^{3}\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 4 u 3 biex tikseb 7.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-3x^{7}\times 12\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Immultiplika 3 u 12 biex tikseb 36.

$$factor(\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-36x^{7}\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{24x\left(x^{3}+1\right)^{\frac{3}{2}}-36x^{7}\left(x^{3}+1\right)^{\frac{3}{2}}}{16\left(x^{3}+1\right)^{\frac{3}{2}}}.

$$factor(\frac{12x\left(x^{3}+1\right)^{\frac{3}{2}}\left(-3x^{6}+2\right)}{16\left(x^{3}+1\right)^{\frac{3}{2}}})$$

Annulla 4\left(x^{3}+1\right)^{\frac{3}{2}} fin-numeratur u d-denominatur.

$$factor(\frac{3x\left(-3x^{6}+2\right)}{4})$$

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

$$factor(\frac{-9x^{7}+6x}{4})$$

Ikkunsidra li -9x^{7}+6x. Iffattura 'l barra 3.

$$3\left(-3x^{7}+2x\right)$$

Ikkunsidra li -3x^{7}+2x. Iffattura 'l barra x.

$$x\left(-3x^{6}+2\right)$$

Erġa' ikteb l-espressjoni ffatturata kompluta. Issimplifika. Polynomial -3x^{6}+2 mhux fatturat billi m'għandux għeruq razzjonali.

$$\frac{3x\left(-3x^{6}+2\right)}{4}$$