Rešite x/x^2-4+2/x^2+4x+4

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

Ovrednoti

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

Kratka navodila za rešitev

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

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-2\right)\left(x+2\right) in \left(x+2\right)^{2} je \left(x-2\right)\left(x+2\right)^{2}. Pomnožite \frac{x}{\left(x-2\right)\left(x+2\right)} s/z \frac{x+2}{x+2}. Pomnožite \frac{2}{\left(x+2\right)^{2}} s/z \frac{x-2}{x-2}.

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

\frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} in \frac{2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v x\left(x+2\right)+2\left(x-2\right).

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

Združite podobne člene v x^{2}+2x+2x-4.

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

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

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

Odvajajte w.r.t. x

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