Issolvi x+2y+4y^2/x-2y-4x^2y/x^2-4y^2

$$x + 2 y + \frac { 4 y ^ { 2 } } { x - 2 y } - \frac { 4 x ^ { 2 } y } { x ^ { 2 } - 4 y ^ { 2 } }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika x+2y b'\frac{x-2y}{x-2y}.

$$\frac{\left(x+2y\right)\left(x-2y\right)}{x-2y}+\frac{4y^{2}}{x-2y}-\frac{4x^{2}y}{x^{2}-4y^{2}}$$

Billi \frac{\left(x+2y\right)\left(x-2y\right)}{x-2y} u \frac{4y^{2}}{x-2y} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(x+2y\right)\left(x-2y\right)+4y^{2}}{x-2y}-\frac{4x^{2}y}{x^{2}-4y^{2}}$$

Agħmel il-multiplikazzjonijiet fi \left(x+2y\right)\left(x-2y\right)+4y^{2}.

$$\frac{x^{2}-2xy+2yx-4y^{2}+4y^{2}}{x-2y}-\frac{4x^{2}y}{x^{2}-4y^{2}}$$

Ikkombina termini simili f'x^{2}-2xy+2yx-4y^{2}+4y^{2}.

$$\frac{x^{2}}{x-2y}-\frac{4x^{2}y}{x^{2}-4y^{2}}$$

Iffattura x^{2}-4y^{2}.

$$\frac{x^{2}}{x-2y}-\frac{4x^{2}y}{\left(x-2y\right)\left(x+2y\right)}$$

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

$$\frac{x^{2}\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}-\frac{4x^{2}y}{\left(x-2y\right)\left(x+2y\right)}$$

Billi \frac{x^{2}\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)} u \frac{4x^{2}y}{\left(x-2y\right)\left(x+2y\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{x^{2}\left(x+2y\right)-4x^{2}y}{\left(x-2y\right)\left(x+2y\right)}$$

Agħmel il-multiplikazzjonijiet fi x^{2}\left(x+2y\right)-4x^{2}y.

$$\frac{x^{3}+2x^{2}y-4x^{2}y}{\left(x-2y\right)\left(x+2y\right)}$$

Ikkombina termini simili f'x^{3}+2x^{2}y-4x^{2}y.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x^{3}-2x^{2}y}{\left(x-2y\right)\left(x+2y\right)}.

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

Annulla x-2y fin-numeratur u d-denominatur.

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

Iddifferenzja w.r.t. x

$$\frac{x\left(x+4y\right)}{\left(x+2y\right)^{2}}$$