Riješi 2/x^2+7x+10+3/x^2-25

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Izračunaj

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Kratki koraci za rješenje

Rastavite x^{2}+7x+10 na faktore. Rastavite x^{2}-25 na faktore.

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

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

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

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

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

Pomnožite izraz 2\left(x-5\right)+3\left(x+2\right).

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Kombinirajte slične izraze u 2x-10+3x+6.

$$\frac{5x-4}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Proširivanje broja \left(x-5\right)\left(x+2\right)\left(x+5\right).

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

Diferenciraj u odnosu na x

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$