Issolvi frac{x^{2}}{x^{2}-y^2}-x/x+y+y/2x-2y-y^2/2x^2-2y^2

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

Evalwa

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura x^{2}-y^{2}.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' \left(x+y\right)\left(x-y\right) u x+y huwa \left(x+y\right)\left(x-y\right). Immultiplika \frac{x}{x+y} b'\frac{x-y}{x-y}.

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

Billi \frac{x^{2}}{\left(x+y\right)\left(x-y\right)} u \frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi x^{2}-x\left(x-y\right).

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

Ikkombina termini simili f'x^{2}-x^{2}+xy.

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

Iffattura 2x-2y.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' \left(x+y\right)\left(x-y\right) u 2\left(x-y\right) huwa 2\left(x+y\right)\left(x-y\right). Immultiplika \frac{xy}{\left(x+y\right)\left(x-y\right)} b'\frac{2}{2}. Immultiplika \frac{y}{2\left(x-y\right)} b'\frac{x+y}{x+y}.

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

Billi \frac{2xy}{2\left(x+y\right)\left(x-y\right)} u \frac{y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi 2xy+y\left(x+y\right).

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

Ikkombina termini simili f'2xy+xy+y^{2}.

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Iffattura 2x^{2}-2y^{2}.

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

Billi \frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)} u \frac{y^{2}}{2\left(x+y\right)\left(x-y\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{y^{2}+3xy-y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

Ikkombina termini simili f'y^{2}+3xy-y^{2}.

$$\frac{3xy}{2\left(x+y\right)\left(x-y\right)}$$

Espandi 2\left(x+y\right)\left(x-y\right).

$$\frac{3xy}{2x^{2}-2y^{2}}$$

Fattur

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$