Riješi x^2/x^2+6x+9-4/x^2-9=

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

Izračunaj

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

Kratki koraci za rješenje

Rastavite x^{2}+6x+9 na faktore. Rastavite x^{2}-9 na faktore.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+3\right)^{2} i \left(x-3\right)\left(x+3\right) jest \left(x-3\right)\left(x+3\right)^{2}. Pomnožite \frac{x^{2}}{\left(x+3\right)^{2}} i \frac{x-3}{x-3}. Pomnožite \frac{4}{\left(x-3\right)\left(x+3\right)} i \frac{x+3}{x+3}.

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

Budući da \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} i \frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x^{2}\left(x-3\right)-4\left(x+3\right).

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

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

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

Diferenciraj u odnosu na x

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