ដោះស្រាយ 1/x^2-1-2/x^2+3x-4+1/x^2-2x-3

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

វាយតម្លៃ

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

ជំហានចម្លើយខ្លីៗ

ដាក់ជាកត្តា x^{2}-1។ ដាក់ជាកត្តា x^{2}+3x-4។

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

ដើម្បីបូក ឬដក​កន្សោម ពន្លាតពួកវាដើម្បីធ្វើឲ្យភាគបែងរបស់ពួកវាដូចគ្នា។ ពហុគុណរួមតូចបំផុតនៃ \left(x-1\right)\left(x+1\right) និង \left(x-1\right)\left(x+4\right) គឺ \left(x-1\right)\left(x+1\right)\left(x+4\right)។ គុណ \frac{1}{\left(x-1\right)\left(x+1\right)} ដង \frac{x+4}{x+4}។ គុណ \frac{2}{\left(x-1\right)\left(x+4\right)} ដង \frac{x+1}{x+1}។

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

ដោយសារ \frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} និង \frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

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

ធ្វើផល​គុណនៅក្នុង x+4-2\left(x+1\right)។

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

បន្សំដូចជាតួនៅក្នុង x+4-2x-2។

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

ដាក់ជាកត្តា x^{2}-2x-3។

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

ដើម្បីបូក ឬដក​កន្សោម ពន្លាតពួកវាដើម្បីធ្វើឲ្យភាគបែងរបស់ពួកវាដូចគ្នា។ ពហុគុណរួមតូចបំផុតនៃ \left(x-1\right)\left(x+1\right)\left(x+4\right) និង \left(x-3\right)\left(x+1\right) គឺ \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)។ គុណ \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} ដង \frac{x-3}{x-3}។ គុណ \frac{1}{\left(x-3\right)\left(x+1\right)} ដង \frac{\left(x-1\right)\left(x+4\right)}{\left(x-1\right)\left(x+4\right)}។

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

ដោយសារ \frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} និង \frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} មានភាគបែងដូចគ្នា សូមបូកពួកវាដោយការបូកភាគយករបស់ពួកវា។

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

ធ្វើផល​គុណនៅក្នុង \left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right)។

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

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

$$\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

ពន្លាត \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)។

$$\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}$$

ធ្វើឌីផេរ៉ងស្យែល w.r.t. x

$$\frac{2\left(43-130x+67x^{2}+12x^{3}-12x^{4}\right)}{\left(\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)\right)^{2}}$$