Riješi x/x-1+2/x+1-x^2+1/x^2-1

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

Procijeni

$$\frac{3}{x+1}$$

Kratki koraci rješenja

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

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

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

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

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

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

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

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

Faktorirajte x^{2}-1.

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

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

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

Izvršite množenja u x^{2}+3x-2-\left(x^{2}+1\right).

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

Kombinirajte slične izraze u x^{2}+3x-2-x^{2}-1.

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

Faktorirajte izraze koji nisu već faktorirani u \frac{3x-3}{\left(x-1\right)\left(x+1\right)}.

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

Otkaži x-1 u brojiocu i imeniocu.

$$\frac{3}{x+1}$$

Proširi

$$\frac{3}{x+1}$$

Kratki koraci rješenja

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

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

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

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

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

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

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

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

Faktorirajte x^{2}-1.

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

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

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

Izvršite množenja u x^{2}+3x-2-\left(x^{2}+1\right).

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

Kombinirajte slične izraze u x^{2}+3x-2-x^{2}-1.

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

Faktorirajte izraze koji nisu već faktorirani u \frac{3x-3}{\left(x-1\right)\left(x+1\right)}.

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

Otkaži x-1 u brojiocu i imeniocu.

$$\frac{3}{x+1}$$