x/2x^2-7x+3+x-3/4x^2+4x-3-x^2+1/2x^2-3x সমাধান কৰক

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

মূল্যায়ন

$$\frac{-4x^{5}+14x^{4}-4x^{3}+26x^{2}-12x-9}{x\left(x-3\right)\left(2x-1\right)\left(4x^{2}-9\right)}$$

সমাধানৰ স্তৰবোৰ সজাওক

উৎপাদক 2x^{2}-7x+3৷ উৎপাদক 4x^{2}+4x-3৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-3\right)\left(2x-1\right) আৰু \left(2x-1\right)\left(2x+3\right)ৰ সাধাৰণ গুণফল হৈছে \left(x-3\right)\left(2x-1\right)\left(2x+3\right)৷ \frac{x}{\left(x-3\right)\left(2x-1\right)} বাৰ \frac{2x+3}{2x+3} পুৰণ কৰক৷ \frac{x-3}{\left(2x-1\right)\left(2x+3\right)} বাৰ \frac{x-3}{x-3} পুৰণ কৰক৷

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

যিহেতু \frac{x\left(2x+3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} আৰু \frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷

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

x\left(2x+3\right)+\left(x-3\right)\left(x-3\right)ত গুণনিয়ক কৰক৷

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

2x^{2}+3x+x^{2}-3x-3x+9ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

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

উৎপাদক 2x^{2}-3x৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-3\right)\left(2x-1\right)\left(2x+3\right) আৰু x\left(2x-3\right)ৰ সাধাৰণ গুণফল হৈছে x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)৷ \frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} বাৰ \frac{x\left(2x-3\right)}{x\left(2x-3\right)} পুৰণ কৰক৷ \frac{x^{2}+1}{x\left(2x-3\right)} বাৰ \frac{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} পুৰণ কৰক৷

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

যিহেতু \frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)} আৰু \frac{\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ বিয়োগ কৰি বিয়োগ কৰক৷

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

\left(3x^{2}-3x+9\right)x\left(2x-3\right)-\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)ত গুণনিয়ক কৰক৷

$$\frac{6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right) বিস্তাৰ কৰক৷

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{8x^{5}-28x^{4}-6x^{3}+63x^{2}-27x}$$

বিস্তাৰ

$$\frac{-4x^{5}+14x^{4}-4x^{3}+26x^{2}-12x-9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)\left(2x^{2}-3x\right)}$$

সমাধানৰ স্তৰবোৰ সজাওক

উৎপাদক 2x^{2}-7x+3৷ উৎপাদক 4x^{2}+4x-3৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-3\right)\left(2x-1\right) আৰু \left(2x-1\right)\left(2x+3\right)ৰ সাধাৰণ গুণফল হৈছে \left(x-3\right)\left(2x-1\right)\left(2x+3\right)৷ \frac{x}{\left(x-3\right)\left(2x-1\right)} বাৰ \frac{2x+3}{2x+3} পুৰণ কৰক৷ \frac{x-3}{\left(2x-1\right)\left(2x+3\right)} বাৰ \frac{x-3}{x-3} পুৰণ কৰক৷

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

যিহেতু \frac{x\left(2x+3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} আৰু \frac{\left(x-3\right)\left(x-3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷

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

x\left(2x+3\right)+\left(x-3\right)\left(x-3\right)ত গুণনিয়ক কৰক৷

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

2x^{2}+3x+x^{2}-3x-3x+9ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

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

উৎপাদক 2x^{2}-3x৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-3\right)\left(2x-1\right)\left(2x+3\right) আৰু x\left(2x-3\right)ৰ সাধাৰণ গুণফল হৈছে x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)৷ \frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} বাৰ \frac{x\left(2x-3\right)}{x\left(2x-3\right)} পুৰণ কৰক৷ \frac{x^{2}+1}{x\left(2x-3\right)} বাৰ \frac{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} পুৰণ কৰক৷

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

যিহেতু \frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)} আৰু \frac{\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ বিয়োগ কৰি বিয়োগ কৰক৷

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

\left(3x^{2}-3x+9\right)x\left(2x-3\right)-\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)ত গুণনিয়ক কৰক৷

$$\frac{6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right) বিস্তাৰ কৰক৷

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{8x^{5}-28x^{4}-6x^{3}+63x^{2}-27x}$$