Riješi 1/x^2-5x+6+1/x^2-3x+2+2/x^2-8x+15

$$\frac { 1 } { x ^ { 2 } - 5 x + 6 } + \frac { 1 } { x ^ { 2 } - 3 x + 2 } + \frac { 2 } { x ^ { 2 } - 8 x + 15 }$$

Izračunaj

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Kratki koraci za rješenje

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

$$\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1+x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Kombinirajte slične izraze u x-1+x-3.

$$\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}.

$$\frac{2\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Skratite x-2 u brojniku i nazivniku.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Rastavite x^{2}-8x+15 na faktore.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{\left(x-5\right)\left(x-3\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x-3\right)\left(x-1\right) i \left(x-5\right)\left(x-3\right) jest \left(x-5\right)\left(x-3\right)\left(x-1\right). Pomnožite \frac{2}{\left(x-3\right)\left(x-1\right)} i \frac{x-5}{x-5}. Pomnožite \frac{2}{\left(x-5\right)\left(x-3\right)} i \frac{x-1}{x-1}.

$$\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}+\frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Budući da \frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} i \frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{2\left(x-5\right)+2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Pomnožite izraz 2\left(x-5\right)+2\left(x-1\right).

$$\frac{2x-10+2x-2}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Kombinirajte slične izraze u 2x-10+2x-2.

$$\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}.

$$\frac{4\left(x-3\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Skratite x-3 u brojniku i nazivniku.

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Proširivanje broja \left(x-5\right)\left(x-1\right).

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

Diferenciraj u odnosu na x

$$\frac{8\left(3-x\right)}{\left(\left(x-5\right)\left(x-1\right)\right)^{2}}$$