Riješi f(x)=(x^2+4x+3/x^2+2x-3-x^2+2x+1/x^2+3x+2)*x+2/x+1

$$f ( x ) = ( \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 2 } + 2 x - 3 } - \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot \frac { x + 2 } { x + 1 }$$

Izračunaj

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

Kratki koraci za rješenje

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

Skratite x+3 u brojniku i nazivniku.

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

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

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

Skratite x+1 u brojniku i nazivniku.

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

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

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

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

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

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

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

Kombinirajte slične izraze u x^{2}+2x+x+2-x^{2}+x-x+1.

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

Pomnožite \frac{3x+3}{\left(x-1\right)\left(x+2\right)} i \frac{x+2}{x+1} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Skratite x+2 u brojniku i nazivniku.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

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

Skratite x+1 u brojniku i nazivniku.

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

Proširi

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

Kratki koraci za rješenje

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

Skratite x+3 u brojniku i nazivniku.

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

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

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

Skratite x+1 u brojniku i nazivniku.

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

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

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

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

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

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

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

Kombinirajte slične izraze u x^{2}+2x+x+2-x^{2}+x-x+1.

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

Pomnožite \frac{3x+3}{\left(x-1\right)\left(x+2\right)} i \frac{x+2}{x+1} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Skratite x+2 u brojniku i nazivniku.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

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

Skratite x+1 u brojniku i nazivniku.

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