Riješi 1/x+3+1/x-1-2

$$\frac { 1 } { x + 3 } + \frac { 1 } { x - 1 } - 2$$

Izračunaj

$$\frac{2\left(4-x-x^{2}\right)}{\left(x-1\right)\left(x+3\right)}$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+3 i x-1 jest \left(x-1\right)\left(x+3\right). Pomnožite \frac{1}{x+3} i \frac{x-1}{x-1}. Pomnožite \frac{1}{x-1} i \frac{x+3}{x+3}.

$$\frac{x-1}{\left(x-1\right)\left(x+3\right)}+\frac{x+3}{\left(x-1\right)\left(x+3\right)}-2$$

Budući da \frac{x-1}{\left(x-1\right)\left(x+3\right)} i \frac{x+3}{\left(x-1\right)\left(x+3\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{x-1+x+3}{\left(x-1\right)\left(x+3\right)}-2$$

Kombinirajte slične izraze u x-1+x+3.

$$\frac{2x+2}{\left(x-1\right)\left(x+3\right)}-2$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Pomnožite 2 i \frac{\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}.

$$\frac{2x+2}{\left(x-1\right)\left(x+3\right)}-\frac{2\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}$$

Budući da \frac{2x+2}{\left(x-1\right)\left(x+3\right)} i \frac{2\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{2x+2-2\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}$$

Pomnožite izraz 2x+2-2\left(x-1\right)\left(x+3\right).

$$\frac{2x+2-2x^{2}-6x+2x+6}{\left(x-1\right)\left(x+3\right)}$$

Kombinirajte slične izraze u 2x+2-2x^{2}-6x+2x+6.

$$\frac{-2x+8-2x^{2}}{\left(x-1\right)\left(x+3\right)}$$

Proširivanje broja \left(x-1\right)\left(x+3\right).

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

Diferenciraj u odnosu na x

$$-\frac{2\left(x^{2}+2x+5\right)}{\left(\left(x-1\right)\left(x+3\right)\right)^{2}}$$