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

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

Luacháil

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

Céimeanna gearra réitigh

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 2 agus 2 chun 4 a bhaint amach.

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

Méadaigh 3 agus 72 chun 216 a fháil.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

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

Cealaigh 8\left(x^{3}+1\right)^{\frac{3}{2}} mar uimhreoir agus ainmneoir.

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

Fairsingigh an slonn.

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

Fachtóirigh

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

Céimeanna Réitigh

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 2 agus 2 chun 4 a bhaint amach.

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

Méadaigh 3 agus 72 chun 216 a fháil.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \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}}}.

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

Cealaigh 8\left(x^{3}+1\right)^{\frac{3}{2}} mar uimhreoir agus ainmneoir.

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

Úsáid an t-airí dáileach chun 3x a mhéadú faoi -9x^{9}-18x^{6}-9x^{3}+1.

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

Mar shampla -27x^{10}-54x^{7}-27x^{4}+3x. Fág 3 as an áireamh.

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

Mar shampla -9x^{10}-18x^{7}-9x^{4}+x. Fág x as an áireamh.

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

Athscríobh an slonn iomlán fachtóirithe. Simpligh. Níl an t-iltéarmach -9x^{9}-18x^{6}-9x^{3}+1 fachtóirithe toisc nach bhfuil aon fhréamh chóimheasta aige.

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