Riješi 2x-3/x+2-x/x+3+1/x=

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

Izračunaj

$$\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}$$

Kratki koraci za rješenje

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

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

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

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

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

$$\frac{2x^{2}+6x-3x-9-x^{2}-2x}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}$$

Kombinirajte slične izraze u 2x^{2}+6x-3x-9-x^{2}-2x.

$$\frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+2\right)\left(x+3\right) i x jest x\left(x+2\right)\left(x+3\right). Pomnožite \frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)} i \frac{x}{x}. Pomnožite \frac{1}{x} i \frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}.

$$\frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)}+\frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}$$

Budući da \frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)} i \frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}$$

Pomnožite izraz \left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right).

$$\frac{x^{3}+x^{2}-9x+x^{2}+3x+2x+6}{x\left(x+2\right)\left(x+3\right)}$$

Kombinirajte slične izraze u x^{3}+x^{2}-9x+x^{2}+3x+2x+6.

$$\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}$$

Proširivanje broja x\left(x+2\right)\left(x+3\right).

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

Proširi

$$\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}$$

Kratki koraci za rješenje

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

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

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

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

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

$$\frac{2x^{2}+6x-3x-9-x^{2}-2x}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}$$

Kombinirajte slične izraze u 2x^{2}+6x-3x-9-x^{2}-2x.

$$\frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+2\right)\left(x+3\right) i x jest x\left(x+2\right)\left(x+3\right). Pomnožite \frac{x^{2}+x-9}{\left(x+2\right)\left(x+3\right)} i \frac{x}{x}. Pomnožite \frac{1}{x} i \frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}.

$$\frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)}+\frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}$$

Budući da \frac{\left(x^{2}+x-9\right)x}{x\left(x+2\right)\left(x+3\right)} i \frac{\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right)}{x\left(x+2\right)\left(x+3\right)}$$

Pomnožite izraz \left(x^{2}+x-9\right)x+\left(x+2\right)\left(x+3\right).

$$\frac{x^{3}+x^{2}-9x+x^{2}+3x+2x+6}{x\left(x+2\right)\left(x+3\right)}$$

Kombinirajte slične izraze u x^{3}+x^{2}-9x+x^{2}+3x+2x+6.

$$\frac{x^{3}+2x^{2}-4x+6}{x\left(x+2\right)\left(x+3\right)}$$

Proširivanje broja x\left(x+2\right)\left(x+3\right).

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