Lahenda 1/x^2-1-2/x^2+3x-4+1/x^2-2x-3

$$\frac { 1 } { x ^ { 2 } - 1 } - \frac { 2 } { x ^ { 2 } + 3 x - 4 } + \frac { 1 } { x ^ { 2 } - 2 x - 3 }$$

Arvuta

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

Lühike lahenduskäik

Tegurda x^{2}-1. Tegurda x^{2}+3x-4.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x-1\right)\left(x+1\right) ja \left(x-1\right)\left(x+4\right) vähim ühiskordne on \left(x-1\right)\left(x+1\right)\left(x+4\right). Korrutage omavahel \frac{1}{\left(x-1\right)\left(x+1\right)} ja \frac{x+4}{x+4}. Korrutage omavahel \frac{2}{\left(x-1\right)\left(x+4\right)} ja \frac{x+1}{x+1}.

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

Kuna murdudel \frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} ja \frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} on sama nimetaja, lahutage nende lugejad.

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

Tehke korrutustehted võrrandis x+4-2\left(x+1\right).

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

Kombineerige sarnased liikmed avaldises x+4-2x-2.

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

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

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x-1\right)\left(x+1\right)\left(x+4\right) ja \left(x-3\right)\left(x+1\right) vähim ühiskordne on \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right). Korrutage omavahel \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} ja \frac{x-3}{x-3}. Korrutage omavahel \frac{1}{\left(x-3\right)\left(x+1\right)} ja \frac{\left(x-1\right)\left(x+4\right)}{\left(x-1\right)\left(x+4\right)}.

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

Kuna murdudel \frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} ja \frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis \left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right).

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

Kombineerige sarnased liikmed avaldises -x^{2}+3x+2x-6+x^{2}+4x-x-4.

$$\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

Laiendage \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right).

$$\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}$$

Diferentseeri x-i järgi

$$\frac{2\left(43-130x+67x^{2}+12x^{3}-12x^{4}\right)}{\left(\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)\right)^{2}}$$