सोडोवचें frac{x^{2}+xy-xz}{(x+y)^{2}-z^{2}}divx/(x+z)^{2-y^2}*xy-y^2-yz/(x-y)^2-z^2

$$\frac { x ^ { 2 } + x y - x z } { ( x + y ) ^ { 2 } - z ^ { 2 } } \div \frac { x } { ( x + z ) ^ { 2 } - y ^ { 2 } } \cdot \frac { x y - y ^ { 2 } - y z } { ( x - y ) ^ { 2 } - z ^ { 2 } }$$

मूल्यांकन करचें

$$y$$

संक्षिप्त समाधान पांवडे

\frac{x}{\left(x+z\right)^{2}-y^{2}} च्या पुरकाक \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} गुणून \frac{x}{\left(x+z\right)^{2}-y^{2}} न \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} क भाग लावचो.

$$\frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}$$

\frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

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

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x\left(x+y+z\right)\left(x+y-z\right) रद्द करचो.

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

\frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\left(x-y+z\right)\times \frac{y\left(x-y-z\right)}{\left(x-y+z\right)\left(x-y-z\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x-y-z रद्द करचो.

$$\left(x-y+z\right)\times \frac{y}{x-y+z}$$

x-y+z आनी x-y+z रद्द करचें.

$$y$$

w.r.t. y चो फरक काडचो

$$1$$

व्यत्पन्नाची व्याख्या वापरून पांवडे

\frac{x}{\left(x+z\right)^{2}-y^{2}} च्या पुरकाक \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} गुणून \frac{x}{\left(x+z\right)^{2}-y^{2}} न \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} क भाग लावचो.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}})$$

\frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x\left(x+y+z\right)\left(x+y-z\right)\left(x-y+z\right)}{x\left(x+y+z\right)\left(x+y-z\right)}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}})$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x\left(x+y+z\right)\left(x+y-z\right) रद्द करचो.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(x-y+z\right)\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}})$$

\frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(x-y+z\right)\times \frac{y\left(x-y-z\right)}{\left(x-y+z\right)\left(x-y-z\right)})$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x-y-z रद्द करचो.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(x-y+z\right)\times \frac{y}{x-y+z})$$

x-y+z आनी x-y+z रद्द करचें.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y)$$

ax^{n} चो व्यत्पन्न nax^{n-1} आसा.

$$y^{1-1}$$

1 तल्यान 1 वजा करची.

$$y^{0}$$

0 सोडून t खंयच्याय शब्दा खातीर, t^{0}=1.

$$1$$