Løs 4/x^2-3x-10+x/x^2-9x+20

$$\frac { 4 } { x ^ { 2 } - 3 x - 10 } + \frac { x } { x ^ { 2 } - 9 x + 20 }$$

Evaluer

$$\frac{\left(x-2\right)\left(x+8\right)}{\left(x-5\right)\left(x-4\right)\left(x+2\right)}$$

Korte løsningstrinn

Faktoriser x^{2}-3x-10. Faktoriser x^{2}-9x+20.

$$\frac{4}{\left(x-5\right)\left(x+2\right)}+\frac{x}{\left(x-5\right)\left(x-4\right)}$$

Hvis du vil legge til eller trekke fra uttrykk, kan du utvide dem for å gjøre nevnerne like. Minste felles multiplum av \left(x-5\right)\left(x+2\right) og \left(x-5\right)\left(x-4\right) er \left(x-5\right)\left(x-4\right)\left(x+2\right). Multipliser \frac{4}{\left(x-5\right)\left(x+2\right)} ganger \frac{x-4}{x-4}. Multipliser \frac{x}{\left(x-5\right)\left(x-4\right)} ganger \frac{x+2}{x+2}.

$$\frac{4\left(x-4\right)}{\left(x-5\right)\left(x-4\right)\left(x+2\right)}+\frac{x\left(x+2\right)}{\left(x-5\right)\left(x-4\right)\left(x+2\right)}$$

Siden \frac{4\left(x-4\right)}{\left(x-5\right)\left(x-4\right)\left(x+2\right)} og \frac{x\left(x+2\right)}{\left(x-5\right)\left(x-4\right)\left(x+2\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

$$\frac{4\left(x-4\right)+x\left(x+2\right)}{\left(x-5\right)\left(x-4\right)\left(x+2\right)}$$

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

$$\frac{4x-16+x^{2}+2x}{\left(x-5\right)\left(x-4\right)\left(x+2\right)}$$

Kombiner like ledd i 4x-16+x^{2}+2x.

$$\frac{6x-16+x^{2}}{\left(x-5\right)\left(x-4\right)\left(x+2\right)}$$

Utvid \left(x-5\right)\left(x-4\right)\left(x+2\right).

$$\frac{6x-16+x^{2}}{x^{3}-7x^{2}+2x+40}$$

Differensier med hensyn til x

$$\frac{272-144x+92x^{2}-12x^{3}-x^{4}}{\left(\left(x-5\right)\left(x-4\right)\left(x+2\right)\right)^{2}}$$