Lutasin ang 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

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

I-evaluate

$$y$$

Maiikling Hakbang sa Solution

I-divide ang \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} gamit ang \frac{x}{\left(x+z\right)^{2}-y^{2}} sa pamamagitan ng pagmu-multiply sa \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} gamit ang reciprocal ng \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

I-factor ang mga expression na hindi pa na-factor sa \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}.

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

I-cancel out ang x\left(x+y+z\right)\left(x+y-z\right) sa parehong numerator at denominator.

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

I-factor ang mga expression na hindi pa na-factor sa \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

I-cancel out ang x-y-z sa parehong numerator at denominator.

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

I-cancel out ang x-y+z at x-y+z.

$$y$$

I-differentiate ang w.r.t. y

$$1$$

Mga Hakbang sa Paggamit ng Definition of a Derivative

I-divide ang \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} gamit ang \frac{x}{\left(x+z\right)^{2}-y^{2}} sa pamamagitan ng pagmu-multiply sa \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} gamit ang reciprocal ng \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

I-factor ang mga expression na hindi pa na-factor sa \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}.

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

I-cancel out ang x\left(x+y+z\right)\left(x+y-z\right) sa parehong numerator at denominator.

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

I-factor ang mga expression na hindi pa na-factor sa \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

I-cancel out ang x-y-z sa parehong numerator at denominator.

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

I-cancel out ang x-y+z at x-y+z.

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

Ang derivative ng ax^{n} ay nax^{n-1}.

$$y^{1-1}$$

I-subtract ang 1 mula sa 1.

$$y^{0}$$

Para sa anumang term na t maliban sa 0, t^{0}=1.

$$1$$