Luacháil
\frac{x+7}{\left(x-2\right)\left(x+1\right)}
Difreálaigh w.r.t. x
\frac{5-14x-x^{2}}{x^{4}-2x^{3}-3x^{2}+4x+4}
Graf
Roinn
Cóipeáladh go dtí an ghearrthaisce
\frac{3\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{2\left(x-2\right)}{\left(x-2\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 x-2 agus x+1 ná \left(x-2\right)\left(x+1\right). Méadaigh \frac{3}{x-2} faoi \frac{x+1}{x+1}. Méadaigh \frac{2}{x+1} faoi \frac{x-2}{x-2}.
\frac{3\left(x+1\right)-2\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
Tá an t-ainmneoir céanna ag \frac{3\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} agus \frac{2\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.
\frac{3x+3-2x+4}{\left(x-2\right)\left(x+1\right)}
Déan iolrúcháin in 3\left(x+1\right)-2\left(x-2\right).
\frac{x+7}{\left(x-2\right)\left(x+1\right)}
Cumaisc téarmaí comhchosúla in: 3x+3-2x+4.
\frac{x+7}{x^{2}-x-2}
Fairsingigh \left(x-2\right)\left(x+1\right)
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{2\left(x-2\right)}{\left(x-2\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 x-2 agus x+1 ná \left(x-2\right)\left(x+1\right). Méadaigh \frac{3}{x-2} faoi \frac{x+1}{x+1}. Méadaigh \frac{2}{x+1} faoi \frac{x-2}{x-2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+1\right)-2\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})
Tá an t-ainmneoir céanna ag \frac{3\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} agus \frac{2\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+3-2x+4}{\left(x-2\right)\left(x+1\right)})
Déan iolrúcháin in 3\left(x+1\right)-2\left(x-2\right).
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{\left(x-2\right)\left(x+1\right)})
Cumaisc téarmaí comhchosúla in: 3x+3-2x+4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{x^{2}+x-2x-2})
Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-2 a iolrú faoi gach téarma de x+1.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{x^{2}-x-2})
Comhcheangail x agus -2x chun -x a fháil.
\frac{\left(x^{2}-x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+7)-\left(x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-2)}{\left(x^{2}-x^{1}-2\right)^{2}}
Do dhá fheidhm indifreáilte ar bith, is ionann díorthach líon an dá fheidhme agus an t-ainmneoir méadaithe faoi dhíorthach an uimhreora lúide an t-uimhreoir méadaithe faoi dhíorthach an ainmneora, agus iad ar fad roinnte faoin ainmneoir cearnaithe.
\frac{\left(x^{2}-x^{1}-2\right)x^{1-1}-\left(x^{1}+7\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.
\frac{\left(x^{2}-x^{1}-2\right)x^{0}-\left(x^{1}+7\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
Simpligh.
\frac{x^{2}x^{0}-x^{1}x^{0}-2x^{0}-\left(x^{1}+7\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
Méadaigh x^{2}-x^{1}-2 faoi x^{0}.
\frac{x^{2}x^{0}-x^{1}x^{0}-2x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-1\right)x^{0}+7\times 2x^{1}+7\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
Méadaigh x^{1}+7 faoi 2x^{1}-x^{0}.
\frac{x^{2}-x^{1}-2x^{0}-\left(2x^{1+1}-x^{1}+7\times 2x^{1}+7\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
Chun cumhachtaí an bhoinn chéanna a mhéadú, suimigh a n-easpónaint.
\frac{x^{2}-x^{1}-2x^{0}-\left(2x^{2}-x^{1}+14x^{1}-7x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
Simpligh.
\frac{-x^{2}-14x^{1}+5x^{0}}{\left(x^{2}-x^{1}-2\right)^{2}}
Cuir téarmaí cosúla le chéile.
\frac{-x^{2}-14x+5x^{0}}{\left(x^{2}-x-2\right)^{2}}
Do théarma ar bith t, t^{1}=t.
\frac{-x^{2}-14x+5\times 1}{\left(x^{2}-x-2\right)^{2}}
Do théarma ar bith t ach amháin 0, t^{0}=1.
\frac{-x^{2}-14x+5}{\left(x^{2}-x-2\right)^{2}}
Do théarma ar bith t, t\times 1=t agus 1t=t.
Samplaí
Cothromóid chearnach
{ x } ^ { 2 } - 4 x - 5 = 0
Triantánacht
4 \sin \theta \cos \theta = 2 \sin \theta
Cothromóid líneach
y = 3x + 4
Uimhríocht
699 * 533
Maitrís
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Cothromóid chomhuaineach
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Difreáil
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Comhtháthú
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Teorainneacha
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}