Løs x-1/x^2+4x+3+2/x^2+5x+6

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

Evaluer

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

Korte løsningstrinn

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

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

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

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

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

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

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

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

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

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

Faktoriser uttrykkene som ikke allerede er faktorisert i \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

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

Eliminer x+3 i både teller og nevner.

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

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

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

Utvid

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

Korte løsningstrinn

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

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

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

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

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

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

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

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

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

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

Faktoriser uttrykkene som ikke allerede er faktorisert i \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}.

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

Eliminer x+3 i både teller og nevner.

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

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

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