মূল্যায়ন
\frac{9x\left(x+1\right)}{8}
বিস্তাৰ
\frac{9x^{2}+9x}{8}
গ্ৰাফ
ভাগ-বতৰা কৰক
ক্লিপবোৰ্ডলৈ প্ৰতিলিপি হৈছে
\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ x+1 আৰু x-2ৰ সাধাৰণ গুণফল হৈছে \left(x-2\right)\left(x+1\right)৷ \frac{x-2}{x+1} বাৰ \frac{x-2}{x-2} পুৰণ কৰক৷ \frac{5-x}{x-2} বাৰ \frac{x+1}{x+1} পুৰণ কৰক৷
\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
যিহেতু \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} আৰু \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷
\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)ত গুণনিয়ক কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
x^{2}-2x-2x+4+5x+5-x^{2}-xৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
উৎপাদক x^{2}-x-2৷ উৎপাদক x^{2}+3x+2৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-2\right)\left(x+1\right) আৰু \left(x+1\right)\left(x+2\right)ৰ সাধাৰণ গুণফল হৈছে \left(x-2\right)\left(x+1\right)\left(x+2\right)৷ \frac{1}{\left(x-2\right)\left(x+1\right)} বাৰ \frac{x+2}{x+2} পুৰণ কৰক৷ \frac{1}{\left(x+1\right)\left(x+2\right)} বাৰ \frac{x-2}{x-2} পুৰণ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
যিহেতু \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} আৰু \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ বিয়োগ কৰি বিয়োগ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
x+2-\left(x-2\right)ত গুণনিয়ক কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
x+2-x+2ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
উৎপাদক x^{2}+x৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ x আৰু x\left(x+1\right)ৰ সাধাৰণ গুণফল হৈছে x\left(x+1\right)৷ \frac{x+1}{x} বাৰ \frac{x+1}{x+1} পুৰণ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}
যিহেতু \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} আৰু \frac{3-x^{2}}{x\left(x+1\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}
\left(x+1\right)\left(x+1\right)+3-x^{2}ত গুণনিয়ক কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}
x^{2}+x+1+x+3-x^{2}ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}
নিউমাৰেটৰ সময়ক নিউমাৰেটৰৰে আৰু ডেনোমিনেটৰ সময়ক ডেনোমিনেটেৰে পূৰণ কৰি \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} বাৰ \frac{2x+4}{x\left(x+1\right)} পূৰণ কৰক৷
\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}
\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}-ৰ ব্যতিক্ৰমৰ দ্বাৰা \frac{9}{\left(x-2\right)\left(x+1\right)} পুৰণ কৰি \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}-ৰ দ্বাৰা \frac{9}{\left(x-2\right)\left(x+1\right)} হৰণ কৰক৷
\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}
নিউমেটৰ আৰু ডেনোমিনেটৰ দুয়োটাতে \left(x-2\right)\left(x+1\right) সমান কৰক৷
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
ইতিমধ্যে উপাদান নোহোৱা ৰাশিবোৰক উপাদান কৰক৷
\frac{9x\left(x+1\right)}{2\times 4}
নিউমেটৰ আৰু ডেনোমিনেটৰ দুয়োটাতে x+2 সমান কৰক৷
\frac{9x^{2}+9x}{8}
ৰাশি বিস্তাৰ কৰক৷
\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ x+1 আৰু x-2ৰ সাধাৰণ গুণফল হৈছে \left(x-2\right)\left(x+1\right)৷ \frac{x-2}{x+1} বাৰ \frac{x-2}{x-2} পুৰণ কৰক৷ \frac{5-x}{x-2} বাৰ \frac{x+1}{x+1} পুৰণ কৰক৷
\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
যিহেতু \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} আৰু \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷
\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)ত গুণনিয়ক কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
x^{2}-2x-2x+4+5x+5-x^{2}-xৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
উৎপাদক x^{2}-x-2৷ উৎপাদক x^{2}+3x+2৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ \left(x-2\right)\left(x+1\right) আৰু \left(x+1\right)\left(x+2\right)ৰ সাধাৰণ গুণফল হৈছে \left(x-2\right)\left(x+1\right)\left(x+2\right)৷ \frac{1}{\left(x-2\right)\left(x+1\right)} বাৰ \frac{x+2}{x+2} পুৰণ কৰক৷ \frac{1}{\left(x+1\right)\left(x+2\right)} বাৰ \frac{x-2}{x-2} পুৰণ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
যিহেতু \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} আৰু \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ বিয়োগ কৰি বিয়োগ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
x+2-\left(x-2\right)ত গুণনিয়ক কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
x+2-x+2ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
উৎপাদক x^{2}+x৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ x আৰু x\left(x+1\right)ৰ সাধাৰণ গুণফল হৈছে x\left(x+1\right)৷ \frac{x+1}{x} বাৰ \frac{x+1}{x+1} পুৰণ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}
যিহেতু \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} আৰু \frac{3-x^{2}}{x\left(x+1\right)}ৰ একে ডেনোমিনেটৰ আছে, গতিকে সিহঁতক সিহঁতৰ নিউমেৰেটৰ যোগ কৰি যোগ কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}
\left(x+1\right)\left(x+1\right)+3-x^{2}ত গুণনিয়ক কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}
x^{2}+x+1+x+3-x^{2}ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}
নিউমাৰেটৰ সময়ক নিউমাৰেটৰৰে আৰু ডেনোমিনেটৰ সময়ক ডেনোমিনেটেৰে পূৰণ কৰি \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} বাৰ \frac{2x+4}{x\left(x+1\right)} পূৰণ কৰক৷
\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}
\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}-ৰ ব্যতিক্ৰমৰ দ্বাৰা \frac{9}{\left(x-2\right)\left(x+1\right)} পুৰণ কৰি \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}-ৰ দ্বাৰা \frac{9}{\left(x-2\right)\left(x+1\right)} হৰণ কৰক৷
\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}
নিউমেটৰ আৰু ডেনোমিনেটৰ দুয়োটাতে \left(x-2\right)\left(x+1\right) সমান কৰক৷
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
ইতিমধ্যে উপাদান নোহোৱা ৰাশিবোৰক উপাদান কৰক৷
\frac{9x\left(x+1\right)}{2\times 4}
নিউমেটৰ আৰু ডেনোমিনেটৰ দুয়োটাতে x+2 সমান কৰক৷
\frac{9x^{2}+9x}{8}
ৰাশি বিস্তাৰ কৰক৷
উদাহৰণসমূহ
দ্বিঘাত সমীকৰণ
{ x } ^ { 2 } - 4 x - 5 = 0
ত্ৰিকোণমিতি
4 \sin \theta \cos \theta = 2 \sin \theta
ৰৈখিক সমীকৰণ
y = 3x + 4
অঙ্ক
699 * 533
মেট্ৰিক্স
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
সমকালীন সমীকৰণ
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
পৃথকীকৰণ
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
ইণ্টিগ্ৰেশ্বন
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
সীমা
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}