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

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

Arvuta

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

Lühike lahenduskäik

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

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

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

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

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

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

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

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

Kombineerige sarnased liikmed avaldises 2x-1-2x+3.

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

Laiendage \left(2x-3\right)\left(2x-1\right)\left(x+1\right).

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

Diferentseeri x-i järgi

$$-\frac{2\left(\left(6x-2\right)^{2}-19\right)}{3\left(\left(2x-3\right)\left(2x-1\right)\left(x+1\right)\right)^{2}}$$