Riješi x^2+8/(x+2)(x-2)+x/x+2-2x/x-2=

$$\frac { x ^ { 2 } + 8 } { ( x + 2 ) ( x - 2 ) } + \frac { x } { x + 2 } - \frac { 2 x } { x - 2 } =$$

Izračunaj

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

Kratki koraci za rješenje

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 x+2 jest \left(x-2\right)\left(x+2\right). Pomnožite \frac{x}{x+2} i \frac{x-2}{x-2}.

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

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

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

Pomnožite izraz x^{2}+8+x\left(x-2\right).

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

Kombinirajte slične izraze u x^{2}+8+x^{2}-2x.

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

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 x-2 jest \left(x-2\right)\left(x+2\right). Pomnožite \frac{2x}{x-2} i \frac{x+2}{x+2}.

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

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

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

Pomnožite izraz 2x^{2}+8-2x-2x\left(x+2\right).

$$\frac{2x^{2}+8-2x-2x^{2}-4x}{\left(x-2\right)\left(x+2\right)}$$

Kombinirajte slične izraze u 2x^{2}+8-2x-2x^{2}-4x.

$$\frac{8-6x}{\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{8-6x}{x^{2}-4}$$

Proširi

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

Kratki koraci za rješenje

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 x+2 jest \left(x-2\right)\left(x+2\right). Pomnožite \frac{x}{x+2} i \frac{x-2}{x-2}.

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

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

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

Pomnožite izraz x^{2}+8+x\left(x-2\right).

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

Kombinirajte slične izraze u x^{2}+8+x^{2}-2x.

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

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 x-2 jest \left(x-2\right)\left(x+2\right). Pomnožite \frac{2x}{x-2} i \frac{x+2}{x+2}.

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

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

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

Pomnožite izraz 2x^{2}+8-2x-2x\left(x+2\right).

$$\frac{2x^{2}+8-2x-2x^{2}-4x}{\left(x-2\right)\left(x+2\right)}$$

Kombinirajte slične izraze u 2x^{2}+8-2x-2x^{2}-4x.

$$\frac{8-6x}{\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{8-6x}{x^{2}-4}$$