Lahenda x/x^2-4+2/x^2+4x+4

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

Arvuta

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

Lühike lahenduskäik

Tegurda x^{2}-4. Tegurda x^{2}+4x+4.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x-2\right)\left(x+2\right) ja \left(x+2\right)^{2} vähim ühiskordne on \left(x-2\right)\left(x+2\right)^{2}. Korrutage omavahel \frac{x}{\left(x-2\right)\left(x+2\right)} ja \frac{x+2}{x+2}. Korrutage omavahel \frac{2}{\left(x+2\right)^{2}} ja \frac{x-2}{x-2}.

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

Kuna murdudel \frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} ja \frac{2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis x\left(x+2\right)+2\left(x-2\right).

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

Kombineerige sarnased liikmed avaldises x^{2}+2x+2x-4.

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

Laiendage \left(x-2\right)\left(x+2\right)^{2}.

$$\frac{x^{2}+4x-4}{x^{3}+2x^{2}-4x-8}$$

Diferentseeri x-i järgi

$$\frac{-x^{3}-6x^{2}+12x-24}{\left(x-2\right)^{2}\left(x+2\right)^{3}}$$