Riješi 1/4x-x^2-4-4/x^2-4+x/2-x+x+1/x+2

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

Izračunaj

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

Kratki koraci za rješenje

Rastavite 4x-x^{2}-4 na faktore. Rastavite x^{2}-4 na faktore.

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

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)\left(-x+2\right). Pomnožite \frac{1}{\left(x-2\right)\left(-x+2\right)} i \frac{x+2}{x+2}. Pomnožite \frac{4}{\left(x-2\right)\left(x+2\right)} i \frac{-x+2}{-x+2}.

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

Budući da \frac{x+2}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} i \frac{4\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x+2-4\left(-x+2\right).

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

Kombinirajte slične izraze u x+2+4x-8.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x}{2-x}+\frac{x+1}{x+2}$$

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)\left(-x+2\right) i 2-x jest \left(x-2\right)\left(x+2\right)\left(-x+2\right). Pomnožite \frac{x}{2-x} i \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Budući da \frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} i \frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{5x-6+x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Pomnožite izraz 5x-6+x\left(x-2\right)\left(x+2\right).

$$\frac{5x-6+x^{3}+2x^{2}-2x^{2}-4x}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Kombinirajte slične izraze u 5x-6+x^{3}+2x^{2}-2x^{2}-4x.

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

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)\left(-x+2\right) i x+2 jest \left(x-2\right)\left(x+2\right)\left(-x+2\right). Pomnožite \frac{x+1}{x+2} i \frac{\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(-x+2\right)}.

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

Budući da \frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} i \frac{\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Pomnožite izraz x-6+x^{3}+\left(x+1\right)\left(x-2\right)\left(-x+2\right).

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

Kombinirajte slične izraze u x-6+x^{3}-x^{3}+4x^{2}-4x-x^{2}+4x-4.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x-10+3x^{2}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}.

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

Skratite x+2 u brojniku i nazivniku.

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

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

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

Proširi

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

Kratki koraci za rješenje

Rastavite 4x-x^{2}-4 na faktore. Rastavite x^{2}-4 na faktore.

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

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)\left(-x+2\right). Pomnožite \frac{1}{\left(x-2\right)\left(-x+2\right)} i \frac{x+2}{x+2}. Pomnožite \frac{4}{\left(x-2\right)\left(x+2\right)} i \frac{-x+2}{-x+2}.

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

Budući da \frac{x+2}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} i \frac{4\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x+2-4\left(-x+2\right).

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

Kombinirajte slične izraze u x+2+4x-8.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x}{2-x}+\frac{x+1}{x+2}$$

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)\left(-x+2\right) i 2-x jest \left(x-2\right)\left(x+2\right)\left(-x+2\right). Pomnožite \frac{x}{2-x} i \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Budući da \frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} i \frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{5x-6+x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Pomnožite izraz 5x-6+x\left(x-2\right)\left(x+2\right).

$$\frac{5x-6+x^{3}+2x^{2}-2x^{2}-4x}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Kombinirajte slične izraze u 5x-6+x^{3}+2x^{2}-2x^{2}-4x.

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

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)\left(-x+2\right) i x+2 jest \left(x-2\right)\left(x+2\right)\left(-x+2\right). Pomnožite \frac{x+1}{x+2} i \frac{\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(-x+2\right)}.

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

Budući da \frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} i \frac{\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Pomnožite izraz x-6+x^{3}+\left(x+1\right)\left(x-2\right)\left(-x+2\right).

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

Kombinirajte slične izraze u x-6+x^{3}-x^{3}+4x^{2}-4x-x^{2}+4x-4.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{x-10+3x^{2}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}.

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

Skratite x+2 u brojniku i nazivniku.

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

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

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