Løs 2/x^2+7x+10+3/x^2-25

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Evaluer

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Korte løsningstrinn

Faktoriser x^{2}+7x+10. Faktoriser x^{2}-25.

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

Hvis du vil legge til eller trekke fra uttrykk, kan du utvide dem for å gjøre nevnerne like. Minste felles multiplum av \left(x+2\right)\left(x+5\right) og \left(x-5\right)\left(x+5\right) er \left(x-5\right)\left(x+2\right)\left(x+5\right). Multipliser \frac{2}{\left(x+2\right)\left(x+5\right)} ganger \frac{x-5}{x-5}. Multipliser \frac{3}{\left(x-5\right)\left(x+5\right)} ganger \frac{x+2}{x+2}.

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

Siden \frac{2\left(x-5\right)}{\left(x-5\right)\left(x+2\right)\left(x+5\right)} og \frac{3\left(x+2\right)}{\left(x-5\right)\left(x+2\right)\left(x+5\right)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

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

Utfør multiplikasjonene i 2\left(x-5\right)+3\left(x+2\right).

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Kombiner like ledd i 2x-10+3x+6.

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

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

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

Differensier med hensyn til x

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$