Réitigh -6/x^2-4x+3-3/3-x-4/x-1

$$\frac{ -6 }{ { x }^{ 2 } -4x+3 } - \frac{ 3 }{ 3-x } - \frac{ 4 }{ x-1 }$$

Luacháil

$$-\frac{1}{x-1}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}-4x+3.

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

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(x-3\right)\left(x-1\right) agus 3-x ná \left(x-3\right)\left(x-1\right). Méadaigh \frac{3}{3-x} faoi \frac{-\left(x-1\right)}{-\left(x-1\right)}.

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

Tá an t-ainmneoir céanna ag \frac{-6}{\left(x-3\right)\left(x-1\right)} agus \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in -6-3\left(-1\right)\left(x-1\right).

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

Cumaisc téarmaí comhchosúla in: -6+3x-3.

$$\frac{-9+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{-9+3x}{\left(x-3\right)\left(x-1\right)}.

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

Cealaigh x-3 mar uimhreoir agus ainmneoir.

$$\frac{3}{x-1}-\frac{4}{x-1}$$

Tá an t-ainmneoir céanna ag \frac{3}{x-1} agus \frac{4}{x-1} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú. Dealaigh 4 ó 3 chun -1 a fháil.

$$\frac{-1}{x-1}$$

Difreálaigh w.r.t. x

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