Lahenda 1/x^2+3x+2+1/x^2-1

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

Arvuta

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

Lühike lahenduskäik

Tegurda x^{2}+3x+2. Tegurda x^{2}-1.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+1\right)\left(x+2\right) ja \left(x-1\right)\left(x+1\right) vähim ühiskordne on \left(x-1\right)\left(x+1\right)\left(x+2\right). Korrutage omavahel \frac{1}{\left(x+1\right)\left(x+2\right)} ja \frac{x-1}{x-1}. Korrutage omavahel \frac{1}{\left(x-1\right)\left(x+1\right)} ja \frac{x+2}{x+2}.

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

Kuna murdudel \frac{x-1}{\left(x-1\right)\left(x+1\right)\left(x+2\right)} ja \frac{x+2}{\left(x-1\right)\left(x+1\right)\left(x+2\right)} on sama nimetaja, liitke nende lugejad.

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

Kombineerige sarnased liikmed avaldises x-1+x+2.

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

Laiendage \left(x-1\right)\left(x+1\right)\left(x+2\right).

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

Diferentseeri x-i järgi

$$-\frac{4x^{3}+7x^{2}+4x+3}{\left(\left(x+2\right)\left(x^{2}-1\right)\right)^{2}}$$