ដោះស្រាយ x/2x^2-7x+3+x-3/4x^2+4x-3-x^2+1/2x^2-3x-9

$$\frac{ x }{ 2 { x }^{ 2 } -7x+3 } + \frac{ x-3 }{ 4 { x }^{ 2 } +4x-3 } - \frac{ { x }^{ 2 } +1 }{ 2 { x }^{ 2 } -3x-9 }$$

វាយតម្លៃ

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

ជំហានចម្លើយខ្លីៗ

ដាក់ជាកត្តា 2x^{2}-7x+3។ ដាក់ជាកត្តា 4x^{2}+4x-3។

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

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

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

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

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

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

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

បន្សំដូចជាតួនៅក្នុង 2x^{2}+3x+x^{2}-3x-3x+9។

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

ដាក់ជាកត្តា 2x^{2}-3x-9។

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

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

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

ដោយសារ \frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} និង \frac{\left(x^{2}+1\right)\left(2x-1\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

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

ធ្វើផល​គុណនៅក្នុង 3x^{2}-3x+9-\left(x^{2}+1\right)\left(2x-1\right)។

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

បន្សំដូចជាតួនៅក្នុង 3x^{2}-3x+9-2x^{3}+x^{2}-2x+1។

$$\frac{4x^{2}-5x+10-2x^{3}}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

ពន្លាត \left(x-3\right)\left(2x-1\right)\left(2x+3\right)។

$$\frac{4x^{2}-5x+10-2x^{3}}{4x^{3}-8x^{2}-15x+9}$$

ពន្លាត

$$\frac{10-5x+4x^{2}-2x^{3}}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

ជំហានចម្លើយខ្លីៗ

ដាក់ជាកត្តា 2x^{2}-7x+3។ ដាក់ជាកត្តា 4x^{2}+4x-3។

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

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

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

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

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

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

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

បន្សំដូចជាតួនៅក្នុង 2x^{2}+3x+x^{2}-3x-3x+9។

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

ដាក់ជាកត្តា 2x^{2}-3x-9។

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

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

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

ដោយសារ \frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} និង \frac{\left(x^{2}+1\right)\left(2x-1\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} មានភាគបែងដូចគ្នា សូមដកពួកវាដោយការដកភាគយករបស់ពួកវា។

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

ធ្វើផល​គុណនៅក្នុង 3x^{2}-3x+9-\left(x^{2}+1\right)\left(2x-1\right)។

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

បន្សំដូចជាតួនៅក្នុង 3x^{2}-3x+9-2x^{3}+x^{2}-2x+1។

$$\frac{4x^{2}-5x+10-2x^{3}}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

ពន្លាត \left(x-3\right)\left(2x-1\right)\left(2x+3\right)។

$$\frac{4x^{2}-5x+10-2x^{3}}{4x^{3}-8x^{2}-15x+9}$$