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

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

Izračunaj

$$y$$

Kratki koraci za rješenje

Podijelite \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} s \frac{x}{\left(x+z\right)^{2}-y^{2}} tako da pomnožite \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} s brojem recipročnim broju \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \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}.

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

Skratite x\left(x+y+z\right)\left(x+y-z\right) u brojniku i nazivniku.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

Skratite x-y-z u brojniku i nazivniku.

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

Skraćivanje x-y+z i x-y+z.

$$y$$

Diferenciraj u odnosu na y

$$1$$

Koraci korištenja definicije derivacije

Podijelite \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} s \frac{x}{\left(x+z\right)^{2}-y^{2}} tako da pomnožite \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} s brojem recipročnim broju \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \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}.

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

Skratite x\left(x+y+z\right)\left(x+y-z\right) u brojniku i nazivniku.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

Skratite x-y-z u brojniku i nazivniku.

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

Skraćivanje x-y+z i x-y+z.

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

Derivacija ax^{n} nax^{n-1}.

$$y^{1-1}$$

Oduzmite 1 od 1.

$$y^{0}$$

Za svaki izraz t osim 0, t^{0}=1.

$$1$$