Riješi 7/x^2-4-5/x^2+4x+4

$$\frac { 7 } { x ^ { 2 } - 4 } - \frac { 5 } { x ^ { 2 } + 4 x + 4 }$$

Izračunaj

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

Kratki koraci za rješenje

Rastavite x^{2}-4 na faktore. Rastavite x^{2}+4x+4 na faktore.

$$\frac{7}{\left(x-2\right)\left(x+2\right)}-\frac{5}{\left(x+2\right)^{2}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x-2\right)\left(x+2\right) i \left(x+2\right)^{2} jest \left(x-2\right)\left(x+2\right)^{2}. Pomnožite \frac{7}{\left(x-2\right)\left(x+2\right)} i \frac{x+2}{x+2}. Pomnožite \frac{5}{\left(x+2\right)^{2}} i \frac{x-2}{x-2}.

$$\frac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Budući da \frac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} i \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{7\left(x+2\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Pomnožite izraz 7\left(x+2\right)-5\left(x-2\right).

$$\frac{7x+14-5x+10}{\left(x-2\right)\left(x+2\right)^{2}}$$

Kombinirajte slične izraze u 7x+14-5x+10.

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

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

$$\frac{2x+24}{x^{3}+2x^{2}-4x-8}$$

Diferenciraj u odnosu na x

$$-\frac{\left(2x+17\right)^{2}-329}{\left(x-2\right)^{2}\left(x+2\right)^{3}}$$