Riješi x-2/x^2-x+1-1/x+1+x^2+x+3/x^3+1

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

Procijeni

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

Kratki koraci rješenja

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva x^{2}-x+1 i x+1 je \left(x+1\right)\left(x^{2}-x+1\right). Pomnožite \frac{x-2}{x^{2}-x+1} i \frac{x+1}{x+1}. Pomnožite \frac{1}{x+1} i \frac{x^{2}-x+1}{x^{2}-x+1}.

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

Pošto \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)} i \frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Izvršite množenja u \left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right).

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

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

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

Faktorirajte x^{3}+1.

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

Pošto \frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)} i \frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

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

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

Faktorirajte izraze koji nisu već faktorirani u \frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}.

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

Otkaži x+1 u brojiocu i imeniocu.

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

Proširi

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

Kratki koraci rješenja

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva x^{2}-x+1 i x+1 je \left(x+1\right)\left(x^{2}-x+1\right). Pomnožite \frac{x-2}{x^{2}-x+1} i \frac{x+1}{x+1}. Pomnožite \frac{1}{x+1} i \frac{x^{2}-x+1}{x^{2}-x+1}.

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

Pošto \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)} i \frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Izvršite množenja u \left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right).

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

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

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

Faktorirajte x^{3}+1.

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

Pošto \frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)} i \frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

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

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

Faktorirajte izraze koji nisu već faktorirani u \frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}.

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

Otkaži x+1 u brojiocu i imeniocu.

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