Løs 1/(x-2)^2+2/x^2-4+1/(x+2)^2

$$\frac { 1 } { ( x - 2 ) ^ { 2 } } + \frac { 2 } { x ^ { 2 } - 4 } + \frac { 1 } { ( x + 2 ) ^ { 2 } }$$

Evaluer

$$4\times \left(\frac{x}{x^{2}-4}\right)^{2}$$

Korte løsningstrinn

Faktoriser x^{2}-4.

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

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

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

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

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

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

$$\frac{x+2+2x-4}{\left(x+2\right)\left(x-2\right)^{2}}+\frac{1}{\left(x+2\right)^{2}}$$

Kombiner like ledd i x+2+2x-4.

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

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

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

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

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

Utfør multiplikasjonene i \left(3x-2\right)\left(x+2\right)+\left(x-2\right)^{2}.

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

Kombiner like ledd i 3x^{2}+6x-2x-4+x^{2}-4x+4.

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

Utvid \left(x-2\right)^{2}\left(x+2\right)^{2}.

$$\frac{4x^{2}}{x^{4}-8x^{2}+16}$$

Utvid

$$4\times \left(\frac{x}{x^{2}-4}\right)^{2}$$

Korte løsningstrinn

Faktoriser x^{2}-4.

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

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

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

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

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

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

$$\frac{x+2+2x-4}{\left(x+2\right)\left(x-2\right)^{2}}+\frac{1}{\left(x+2\right)^{2}}$$

Kombiner like ledd i x+2+2x-4.

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

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

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

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

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

Utfør multiplikasjonene i \left(3x-2\right)\left(x+2\right)+\left(x-2\right)^{2}.

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

Kombiner like ledd i 3x^{2}+6x-2x-4+x^{2}-4x+4.

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

Utvid \left(x-2\right)^{2}\left(x+2\right)^{2}.

$$\frac{4x^{2}}{x^{4}-8x^{2}+16}$$