Réitigh 1/2x^2-x-3-1/2x^2+x-1

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

Luacháil

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

Céimeanna gearra réitigh

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

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(2x-3\right)\left(x+1\right) agus \left(2x-1\right)\left(x+1\right) ná \left(2x-3\right)\left(2x-1\right)\left(x+1\right). Méadaigh \frac{1}{\left(2x-3\right)\left(x+1\right)} faoi \frac{2x-1}{2x-1}. Méadaigh \frac{1}{\left(2x-1\right)\left(x+1\right)} faoi \frac{2x-3}{2x-3}.

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

Tá an t-ainmneoir céanna ag \frac{2x-1}{\left(2x-3\right)\left(2x-1\right)\left(x+1\right)} agus \frac{2x-3}{\left(2x-3\right)\left(2x-1\right)\left(x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in 2x-1-\left(2x-3\right).

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

Cumaisc téarmaí comhchosúla in: 2x-1-2x+3.

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

Fairsingigh \left(2x-3\right)\left(2x-1\right)\left(x+1\right)

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

Difreálaigh w.r.t. x

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