ដោះស្រាយ x^3-2x(x+1/x^3-1

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

វាយតម្លៃ

$$\frac{x\left(x^{5}-x^{2}-2x-2\right)}{x^{3}-1}$$

ជំហានចម្លើយខ្លីៗ

ដាក់ជាកត្តា x^{3}-1។

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

ដើម្បីបូក ឬដក​កន្សោម ពន្លាតពួកវាដើម្បីធ្វើឲ្យភាគបែងរបស់ពួកវាដូចគ្នា។ គុណ x^{3} ដង \frac{\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}។

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

ដោយសារ \frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} និង \frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

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

ធ្វើផល​គុណនៅក្នុង x^{3}\left(x-1\right)\left(x^{2}+x+1\right)-2x\left(x+1\right)។

$$\frac{x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x}{\left(x-1\right)\left(x^{2}+x+1\right)}$$

បន្សំដូចជាតួនៅក្នុង x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x។

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

ពន្លាត \left(x-1\right)\left(x^{2}+x+1\right)។

$$\frac{-2x+x^{6}-x^{3}-2x^{2}}{x^{3}-1}$$

ពន្លាត

$$\frac{x^{6}-x^{3}-2x^{2}-2x}{x^{3}-1}$$

ជំហានចម្លើយខ្លីៗ

ដាក់ជាកត្តា x^{3}-1។

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

ដើម្បីបូក ឬដក​កន្សោម ពន្លាតពួកវាដើម្បីធ្វើឲ្យភាគបែងរបស់ពួកវាដូចគ្នា។ គុណ x^{3} ដង \frac{\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}។

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

ដោយសារ \frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} និង \frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

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

ធ្វើផល​គុណនៅក្នុង x^{3}\left(x-1\right)\left(x^{2}+x+1\right)-2x\left(x+1\right)។

$$\frac{x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x}{\left(x-1\right)\left(x^{2}+x+1\right)}$$

បន្សំដូចជាតួនៅក្នុង x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x។

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

ពន្លាត \left(x-1\right)\left(x^{2}+x+1\right)។

$$\frac{-2x+x^{6}-x^{3}-2x^{2}}{x^{3}-1}$$