x-y/x+y-x+y/x-y/1-frac{x^2-xy-y^2{x^2-y^2}} সমাধান কৰক

$$\frac { \frac { x - y } { x + y } - \frac { x + y } { x - y } } { 1 - \frac { x ^ { 2 } - x y - y ^ { 2 } } { x ^ { 2 } - y ^ { 2 } } }$$

মূল্যায়ন

$$-4$$

সমাধানৰ স্তৰবোৰ সজাওক

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

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

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

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

\left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right)ত গুণনিয়ক কৰক৷

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

x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

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

উৎপাদক x^{2}-y^{2}৷

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

এক্সপ্ৰেশ্বন যোগ বা বিয়োগ কৰিবলৈ, সিহঁতৰ হৰ একে কৰিবলৈ বিস্তাৰ কৰক৷ 1 বাৰ \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} পুৰণ কৰক৷

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}-\frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

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

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{\left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right)}{\left(x+y\right)\left(x-y\right)}}$$

\left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right)ত গুণনিয়ক কৰক৷

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}ৰ একেধৰণ পদবোৰ একত্ৰিত কৰক৷

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{xy}{\left(x+y\right)\left(x-y\right)}}$$

\frac{xy}{\left(x+y\right)\left(x-y\right)}-ৰ ব্যতিক্ৰমৰ দ্বাৰা \frac{-4xy}{\left(x+y\right)\left(x-y\right)} পুৰণ কৰি \frac{xy}{\left(x+y\right)\left(x-y\right)}-ৰ দ্বাৰা \frac{-4xy}{\left(x+y\right)\left(x-y\right)} হৰণ কৰক৷

$$\frac{-4xy\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)xy}$$

নিউমেটৰ আৰু ডেনোমিনেটৰ দুয়োটাতে xy\left(x+y\right)\left(x-y\right) সমান কৰক৷

$$-4$$

কাৰক

$$-4$$