Riješi x-1/x^2+4x+3+2/x^2+5x+6

$$\frac { x - 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 2 } { x ^ { 2 } + 5 x + 6 }$$

Procijeni

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

Kratki koraci rješenja

Faktorirajte x^{2}+4x+3. Faktorirajte x^{2}+5x+6.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x+1\right)\left(x+3\right) i \left(x+2\right)\left(x+3\right) je \left(x+1\right)\left(x+2\right)\left(x+3\right). Pomnožite \frac{x-1}{\left(x+1\right)\left(x+3\right)} i \frac{x+2}{x+2}. Pomnožite \frac{2}{\left(x+2\right)\left(x+3\right)} i \frac{x+1}{x+1}.

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

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

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

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

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

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

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

Faktorirajte izraze koji nisu već faktorirani u \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

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

Otkaži x+3 u brojiocu i imeniocu.

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

Proširite \left(x+1\right)\left(x+2\right).

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

Proširi

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

Kratki koraci rješenja

Faktorirajte x^{2}+4x+3. Faktorirajte x^{2}+5x+6.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x+1\right)\left(x+3\right) i \left(x+2\right)\left(x+3\right) je \left(x+1\right)\left(x+2\right)\left(x+3\right). Pomnožite \frac{x-1}{\left(x+1\right)\left(x+3\right)} i \frac{x+2}{x+2}. Pomnožite \frac{2}{\left(x+2\right)\left(x+3\right)} i \frac{x+1}{x+1}.

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

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

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

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

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

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

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

Faktorirajte izraze koji nisu već faktorirani u \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

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

Otkaži x+3 u brojiocu i imeniocu.

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

Proširite \left(x+1\right)\left(x+2\right).

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