Riješi x+1+3x/x^2-x-6

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

Procijeni

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

Kratki koraci rješenja

Faktorirajte x^{2}-x-6.

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

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

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

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

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

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

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

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

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

Proširite \left(x-3\right)\left(x+2\right).

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

Razlikovanje u pogledu x

$$\frac{x^{4}-2x^{3}-14x^{2}+12x+18}{\left(\left(x-3\right)\left(x+2\right)\right)^{2}}$$