Riješi x+1/(x+7)-x/x(x-2)

$$\frac { x + 1 } { ( x + 7 ) } - \frac { x } { x ( x - 2 ) }$$

Izračunaj

$$\frac{x^{2}-2x-9}{\left(x-2\right)\left(x+7\right)}$$

Kratki koraci za rješenje

Skratite x u brojniku i nazivniku.

$$\frac{x+1}{x+7}-\frac{1}{x-2}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+7 i x-2 jest \left(x-2\right)\left(x+7\right). Pomnožite \frac{x+1}{x+7} i \frac{x-2}{x-2}. Pomnožite \frac{1}{x-2} i \frac{x+7}{x+7}.

$$\frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+7\right)}-\frac{x+7}{\left(x-2\right)\left(x+7\right)}$$

Budući da \frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+7\right)} i \frac{x+7}{\left(x-2\right)\left(x+7\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\left(x+1\right)\left(x-2\right)-\left(x+7\right)}{\left(x-2\right)\left(x+7\right)}$$

Pomnožite izraz \left(x+1\right)\left(x-2\right)-\left(x+7\right).

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

Kombinirajte slične izraze u x^{2}-2x+x-2-x-7.

$$\frac{x^{2}-2x-9}{\left(x-2\right)\left(x+7\right)}$$

Proširivanje broja \left(x-2\right)\left(x+7\right).

$$\frac{x^{2}-2x-9}{x^{2}+5x-14}$$

Proširi

$$\frac{x^{2}-2x-9}{\left(x-2\right)\left(x+7\right)}$$

Kratki koraci za rješenje

Skratite x u brojniku i nazivniku.

$$\frac{x+1}{x+7}-\frac{1}{x-2}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+7 i x-2 jest \left(x-2\right)\left(x+7\right). Pomnožite \frac{x+1}{x+7} i \frac{x-2}{x-2}. Pomnožite \frac{1}{x-2} i \frac{x+7}{x+7}.

$$\frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+7\right)}-\frac{x+7}{\left(x-2\right)\left(x+7\right)}$$

Budući da \frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+7\right)} i \frac{x+7}{\left(x-2\right)\left(x+7\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\left(x+1\right)\left(x-2\right)-\left(x+7\right)}{\left(x-2\right)\left(x+7\right)}$$

Pomnožite izraz \left(x+1\right)\left(x-2\right)-\left(x+7\right).

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

Kombinirajte slične izraze u x^{2}-2x+x-2-x-7.

$$\frac{x^{2}-2x-9}{\left(x-2\right)\left(x+7\right)}$$

Proširivanje broja \left(x-2\right)\left(x+7\right).

$$\frac{x^{2}-2x-9}{x^{2}+5x-14}$$