Løs x+1+3x/x^2-x-6

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

Evaluer

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

Korte løsningstrinn

Faktoriser x^{2}-x-6.

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

Hvis du vil legge til eller trekke fra uttrykk, kan du utvide dem for å gjøre nevnerne like. Multipliser x+1 ganger \frac{\left(x-3\right)\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}.

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

Siden \frac{\left(x+1\right)\left(x-3\right)\left(x+2\right)}{\left(x-3\right)\left(x+2\right)} og \frac{3x}{\left(x-3\right)\left(x+2\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

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

Utfør multiplikasjonene i \left(x+1\right)\left(x-3\right)\left(x+2\right)+3x.

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

Kombiner like ledd i x^{3}-x^{2}-6x+x^{2}-x-6+3x.

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

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

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

Differensier med hensyn til x

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