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

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

মূল্যায়ন

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

সমাধানৰ স্তৰবোৰ সজাওক

উৎপাদক x^{2}-1৷ উৎপাদক x^{2}+3x-4৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-1\right)\left(x+1\right) আৰু \left(x-1\right)\left(x+4\right)ৰ সাধাৰণ গুণফল হৈছে \left(x-1\right)\left(x+1\right)\left(x+4\right)৷ \frac{1}{\left(x-1\right)\left(x+1\right)} বাৰ \frac{x+4}{x+4} পুৰণ কৰক৷ \frac{2}{\left(x-1\right)\left(x+4\right)} বাৰ \frac{x+1}{x+1} পুৰণ কৰক৷

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

যিহেতু \frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} আৰু \frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ বিয়োগ কৰি বিয়োগ কৰক৷

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

x+4-2\left(x+1\right)ত গুণনিয়ক কৰক৷

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

x+4-2x-2ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

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

উৎপাদক x^{2}-2x-3৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-1\right)\left(x+1\right)\left(x+4\right) আৰু \left(x-3\right)\left(x+1\right)ৰ সাধাৰণ গুণফল হৈছে \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)৷ \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} বাৰ \frac{x-3}{x-3} পুৰণ কৰক৷ \frac{1}{\left(x-3\right)\left(x+1\right)} বাৰ \frac{\left(x-1\right)\left(x+4\right)}{\left(x-1\right)\left(x+4\right)} পুৰণ কৰক৷

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

যিহেতু \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)} আৰু \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)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷

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

\left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right)ত গুণনিয়ক কৰক৷

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

-x^{2}+3x+2x-6+x^{2}+4x-x-4ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

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

\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right) বিস্তাৰ কৰক৷

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

ডিফাৰেনচিয়েট w.r.t. x

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