Løs 1/4x-x^2-4-4/x^2-4+x/2-x+x+1/x+2

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

Evaluer

$$\frac{5-3x}{\left(2-x\right)^{2}}$$

Korte løsningstrinn

Faktoriser 4x-x^{2}-4. Faktoriser x^{2}-4.

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

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) og \left(x-2\right)\left(x+2\right) er \left(x-2\right)\left(x+2\right)\left(-x+2\right). Multipliser \frac{1}{\left(x-2\right)\left(-x+2\right)} ganger \frac{x+2}{x+2}. Multipliser \frac{4}{\left(x-2\right)\left(x+2\right)} ganger \frac{-x+2}{-x+2}.

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

Siden \frac{x+2}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} og \frac{4\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} har samme nevner, kan du subtrahere dem ved å subtrahere tellerne.

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

Utfør multiplikasjonene i x+2-4\left(-x+2\right).

$$\frac{x+2+4x-8}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x}{2-x}+\frac{x+1}{x+2}$$

Kombiner like ledd i x+2+4x-8.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x}{2-x}+\frac{x+1}{x+2}$$

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)\left(-x+2\right) og 2-x er \left(x-2\right)\left(x+2\right)\left(-x+2\right). Multipliser \frac{x}{2-x} ganger \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Siden \frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} og \frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

$$\frac{5x-6+x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Utfør multiplikasjonene i 5x-6+x\left(x-2\right)\left(x+2\right).

$$\frac{5x-6+x^{3}+2x^{2}-2x^{2}-4x}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Kombiner like ledd i 5x-6+x^{3}+2x^{2}-2x^{2}-4x.

$$\frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

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)\left(-x+2\right) og x+2 er \left(x-2\right)\left(x+2\right)\left(-x+2\right). Multipliser \frac{x+1}{x+2} ganger \frac{\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(-x+2\right)}.

$$\frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Siden \frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} og \frac{\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

$$\frac{x-6+x^{3}+\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Utfør multiplikasjonene i x-6+x^{3}+\left(x+1\right)\left(x-2\right)\left(-x+2\right).

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

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

$$\frac{x-10+3x^{2}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Faktoriser uttrykkene som ikke allerede er faktorisert i \frac{x-10+3x^{2}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}.

$$\frac{\left(3x-5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Eliminer x+2 i både teller og nevner.

$$\frac{3x-5}{\left(x-2\right)\left(-x+2\right)}$$

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

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

Utvid

$$-\frac{3x-5}{\left(x-2\right)^{2}}$$

Korte løsningstrinn

Faktoriser 4x-x^{2}-4. Faktoriser x^{2}-4.

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

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) og \left(x-2\right)\left(x+2\right) er \left(x-2\right)\left(x+2\right)\left(-x+2\right). Multipliser \frac{1}{\left(x-2\right)\left(-x+2\right)} ganger \frac{x+2}{x+2}. Multipliser \frac{4}{\left(x-2\right)\left(x+2\right)} ganger \frac{-x+2}{-x+2}.

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

Siden \frac{x+2}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} og \frac{4\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} har samme nevner, kan du subtrahere dem ved å subtrahere tellerne.

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

Utfør multiplikasjonene i x+2-4\left(-x+2\right).

$$\frac{x+2+4x-8}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x}{2-x}+\frac{x+1}{x+2}$$

Kombiner like ledd i x+2+4x-8.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x}{2-x}+\frac{x+1}{x+2}$$

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)\left(-x+2\right) og 2-x er \left(x-2\right)\left(x+2\right)\left(-x+2\right). Multipliser \frac{x}{2-x} ganger \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.

$$\frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Siden \frac{5x-6}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} og \frac{x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

$$\frac{5x-6+x\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Utfør multiplikasjonene i 5x-6+x\left(x-2\right)\left(x+2\right).

$$\frac{5x-6+x^{3}+2x^{2}-2x^{2}-4x}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

Kombiner like ledd i 5x-6+x^{3}+2x^{2}-2x^{2}-4x.

$$\frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{x+1}{x+2}$$

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)\left(-x+2\right) og x+2 er \left(x-2\right)\left(x+2\right)\left(-x+2\right). Multipliser \frac{x+1}{x+2} ganger \frac{\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(-x+2\right)}.

$$\frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}+\frac{\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Siden \frac{x-6+x^{3}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} og \frac{\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

$$\frac{x-6+x^{3}+\left(x+1\right)\left(x-2\right)\left(-x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Utfør multiplikasjonene i x-6+x^{3}+\left(x+1\right)\left(x-2\right)\left(-x+2\right).

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

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

$$\frac{x-10+3x^{2}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Faktoriser uttrykkene som ikke allerede er faktorisert i \frac{x-10+3x^{2}}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}.

$$\frac{\left(3x-5\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(-x+2\right)}$$

Eliminer x+2 i både teller og nevner.

$$\frac{3x-5}{\left(x-2\right)\left(-x+2\right)}$$

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

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