Riješi x-1/x^2+4x+3+2/x^2+5x+6

$$\frac { x - 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 2 } { x ^ { 2 } + 5 x + 6 }$$

Izračunaj

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

Kratki koraci za rješenje

Rastavite x^{2}+4x+3 na faktore. Rastavite x^{2}+5x+6 na faktore.

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

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

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

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

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

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

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

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

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

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

Skratite x+3 u brojniku i nazivniku.

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

Proširivanje broja \left(x+1\right)\left(x+2\right).

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

Proširi

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

Kratki koraci za rješenje

Rastavite x^{2}+4x+3 na faktore. Rastavite x^{2}+5x+6 na faktore.

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

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

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

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

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

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

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

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

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

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

Skratite x+3 u brojniku i nazivniku.

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

Proširivanje broja \left(x+1\right)\left(x+2\right).

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