Riješi 8/x^2-9-5/x^2+6x+9

$$\frac { 8 } { x ^ { 2 } - 9 } - \frac { 5 } { x ^ { 2 } + 6 x + 9 }$$

Izračunaj

$$\frac{3\left(x+13\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Kratki koraci za rješenje

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

$$\frac{8}{\left(x-3\right)\left(x+3\right)}-\frac{5}{\left(x+3\right)^{2}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x-3\right)\left(x+3\right) i \left(x+3\right)^{2} jest \left(x-3\right)\left(x+3\right)^{2}. Pomnožite \frac{8}{\left(x-3\right)\left(x+3\right)} i \frac{x+3}{x+3}. Pomnožite \frac{5}{\left(x+3\right)^{2}} i \frac{x-3}{x-3}.

$$\frac{8\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Budući da \frac{8\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} i \frac{5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{8\left(x+3\right)-5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Pomnožite izraz 8\left(x+3\right)-5\left(x-3\right).

$$\frac{8x+24-5x+15}{\left(x-3\right)\left(x+3\right)^{2}}$$

Kombinirajte slične izraze u 8x+24-5x+15.

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

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

$$\frac{3x+39}{x^{3}+3x^{2}-9x-27}$$

Diferenciraj u odnosu na x

$$-\frac{6\left(\left(x+9\right)^{2}-96\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$