Riješi x-1/x^2+3x+2+6/2+x-x^2-10-x/4-x^2

$$\frac { x - 1 } { x ^ { 2 } + 3 x + 2 } + \frac { 6 } { 2 + x - x ^ { 2 } } - \frac { 10 - x } { 4 - x ^ { 2 } }$$

Izračunaj

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Kratki koraci za rješenje

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

$$\frac{x-1}{\left(x+1\right)\left(x+2\right)}+\frac{6}{\left(x-2\right)\left(-x-1\right)}-\frac{10-x}{4-x^{2}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+1\right)\left(x+2\right) i \left(x-2\right)\left(-x-1\right) jest \left(x-2\right)\left(x+1\right)\left(x+2\right). Pomnožite \frac{x-1}{\left(x+1\right)\left(x+2\right)} i \frac{x-2}{x-2}. Pomnožite \frac{6}{\left(x-2\right)\left(-x-1\right)} i \frac{-\left(x+2\right)}{-\left(x+2\right)}.

$$\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}+\frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Budući da \frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} i \frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Pomnožite izraz \left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right).

$$\frac{x^{2}-2x-x+2-6x-12}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Kombinirajte slične izraze u x^{2}-2x-x+2-6x-12.

$$\frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}.

$$\frac{\left(x-10\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Skratite x+1 u brojniku i nazivniku.

$$\frac{x-10}{\left(x-2\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Rastavite 4-x^{2} na faktore.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x-2\right)\left(x+2\right) i \left(x-2\right)\left(-x-2\right) jest \left(x-2\right)\left(x+2\right). Pomnožite \frac{10-x}{\left(x-2\right)\left(-x-2\right)} i \frac{-1}{-1}.

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

Budući da \frac{x-10}{\left(x-2\right)\left(x+2\right)} i \frac{-\left(10-x\right)}{\left(x-2\right)\left(x+2\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x-10-\left(-\left(10-x\right)\right).

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

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

$$\frac{0}{\left(x-2\right)\left(x+2\right)}$$

Nula podijeljena s bilo kojim izrazom koji nije nula daje nulu.

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Faktor

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