Riješi 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

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

Procijeni

$$y$$

Kratki koraci rješenja

Podijelite \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} sa \frac{x}{\left(x+z\right)^{2}-y^{2}} tako što ćete pomnožiti \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} recipročnom vrijednošću od \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

Faktorirajte izraze koji nisu već faktorirani u \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}.

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

Otkaži x\left(x+y+z\right)\left(x+y-z\right) u brojiocu i imeniocu.

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

Faktorirajte izraze koji nisu već faktorirani u \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

Otkaži x-y-z u brojiocu i imeniocu.

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

Otkaži x-y+z i x-y+z.

$$y$$

Razlikovanje u pogledu y

$$1$$

Koraci pomoću definicije izvedenog broja

Podijelite \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} sa \frac{x}{\left(x+z\right)^{2}-y^{2}} tako što ćete pomnožiti \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} recipročnom vrijednošću od \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

Faktorirajte izraze koji nisu već faktorirani u \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}.

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

Otkaži x\left(x+y+z\right)\left(x+y-z\right) u brojiocu i imeniocu.

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

Faktorirajte izraze koji nisu već faktorirani u \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

Otkaži x-y-z u brojiocu i imeniocu.

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

Otkaži x-y+z i x-y+z.

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

Izvedena vrijednost broja ax^{n} je nax^{n-1}.

$$y^{1-1}$$

Oduzmite 1 od 1.

$$y^{0}$$

Za bilo koji izraz t izuzev 0, t^{0}=1.

$$1$$