Rešite x^2/x^2+6x+9-4/x^2-9=

$$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 } - \frac { 4 } { x ^ { 2 } - 9 } =$$

Ovrednoti

$$\frac{x^{3}-3x^{2}-4x-12}{\left(x-3\right)\left(x+3\right)^{2}}$$

Kratka navodila za rešitev

Faktorizirajte x^{2}+6x+9. Faktorizirajte x^{2}-9.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x+3\right)^{2} in \left(x-3\right)\left(x+3\right) je \left(x-3\right)\left(x+3\right)^{2}. Pomnožite \frac{x^{2}}{\left(x+3\right)^{2}} s/z \frac{x-3}{x-3}. Pomnožite \frac{4}{\left(x-3\right)\left(x+3\right)} s/z \frac{x+3}{x+3}.

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

Ker \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} in \frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v x^{2}\left(x-3\right)-4\left(x+3\right).

$$\frac{x^{3}-3x^{2}-4x-12}{\left(x-3\right)\left(x+3\right)^{2}}$$

Razčlenite \left(x-3\right)\left(x+3\right)^{2}.

$$\frac{x^{3}-3x^{2}-4x-12}{x^{3}+3x^{2}-9x-27}$$

Odvajajte w.r.t. x

$$\frac{2x\left(3x^{2}-14x+39\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$