Réitigh (1/x^{4-x^{3}}-1/x^4+x^3)*x^2-1/2+1/x^2

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

Luacháil

$$\frac{x+1}{x^{3}}$$

Céimeanna gearra réitigh

Fachtóirigh x^{4}-x^{3}. Fachtóirigh x^{4}+x^{3}.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-1\right)x^{3} agus \left(x+1\right)x^{3} ná \left(x-1\right)\left(x+1\right)x^{3}. Méadaigh \frac{1}{\left(x-1\right)x^{3}} faoi \frac{x+1}{x+1}. Méadaigh \frac{1}{\left(x+1\right)x^{3}} faoi \frac{x-1}{x-1}.

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

Tá an t-ainmneoir céanna ag \frac{x+1}{\left(x-1\right)\left(x+1\right)x^{3}} agus \frac{x-1}{\left(x-1\right)\left(x+1\right)x^{3}} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in x+1-\left(x-1\right).

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

Cumaisc téarmaí comhchosúla in: x+1-x+1.

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

Méadaigh \frac{2}{\left(x-1\right)\left(x+1\right)x^{3}} faoi \frac{x^{2}-1}{2} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

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

Cealaigh 2 mar uimhreoir agus ainmneoir.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-1\right)\left(x+1\right)x^{3} agus x^{2} ná \left(x-1\right)\left(x+1\right)x^{3}. Méadaigh \frac{1}{x^{2}} faoi \frac{x\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)\left(x+1\right)}.

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

Tá an t-ainmneoir céanna ag \frac{x^{2}-1}{\left(x-1\right)\left(x+1\right)x^{3}} agus \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{3}} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Déan iolrúcháin in x^{2}-1+x\left(x-1\right)\left(x+1\right).

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

Cumaisc téarmaí comhchosúla in: x^{2}-1+x^{3}+x^{2}-x^{2}-x.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x^{2}-1+x^{3}-x}{\left(x-1\right)\left(x+1\right)x^{3}}.

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

Cealaigh \left(x-1\right)\left(x+1\right) mar uimhreoir agus ainmneoir.

$$\frac{x+1}{x^{3}}$$

Fairsingigh

$$\frac{x+1}{x^{3}}$$

Céimeanna gearra réitigh

Fachtóirigh x^{4}-x^{3}. Fachtóirigh x^{4}+x^{3}.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-1\right)x^{3} agus \left(x+1\right)x^{3} ná \left(x-1\right)\left(x+1\right)x^{3}. Méadaigh \frac{1}{\left(x-1\right)x^{3}} faoi \frac{x+1}{x+1}. Méadaigh \frac{1}{\left(x+1\right)x^{3}} faoi \frac{x-1}{x-1}.

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

Tá an t-ainmneoir céanna ag \frac{x+1}{\left(x-1\right)\left(x+1\right)x^{3}} agus \frac{x-1}{\left(x-1\right)\left(x+1\right)x^{3}} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in x+1-\left(x-1\right).

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

Cumaisc téarmaí comhchosúla in: x+1-x+1.

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

Méadaigh \frac{2}{\left(x-1\right)\left(x+1\right)x^{3}} faoi \frac{x^{2}-1}{2} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

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

Cealaigh 2 mar uimhreoir agus ainmneoir.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-1\right)\left(x+1\right)x^{3} agus x^{2} ná \left(x-1\right)\left(x+1\right)x^{3}. Méadaigh \frac{1}{x^{2}} faoi \frac{x\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)\left(x+1\right)}.

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

Tá an t-ainmneoir céanna ag \frac{x^{2}-1}{\left(x-1\right)\left(x+1\right)x^{3}} agus \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{3}} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Déan iolrúcháin in x^{2}-1+x\left(x-1\right)\left(x+1\right).

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

Cumaisc téarmaí comhchosúla in: x^{2}-1+x^{3}+x^{2}-x^{2}-x.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x^{2}-1+x^{3}-x}{\left(x-1\right)\left(x+1\right)x^{3}}.

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

Cealaigh \left(x-1\right)\left(x+1\right) mar uimhreoir agus ainmneoir.

$$\frac{x+1}{x^{3}}$$