Evaluer
\frac{2\left(4x-5\right)}{\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)}
Differensier med hensyn til x
\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}}
Graf
Aksje
Kopiert til utklippstavle
\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}
Faktoriser x^{2}-1. Faktoriser x^{2}+3x-4.
\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}
Hvis du vil legge til eller trekke fra uttrykk, kan du utvide dem for å gjøre nevnerne like. Minste felles multiplum av \left(x-1\right)\left(x+1\right) og \left(x-1\right)\left(x+4\right) er \left(x-1\right)\left(x+1\right)\left(x+4\right). Multipliser \frac{1}{\left(x-1\right)\left(x+1\right)} ganger \frac{x+4}{x+4}. Multipliser \frac{2}{\left(x-1\right)\left(x+4\right)} ganger \frac{x+1}{x+1}.
\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}
Siden \frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} og \frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} har samme nevner, kan du subtrahere dem ved å subtrahere tellerne.
\frac{x+4-2x-2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
Utfør multiplikasjonene i x+4-2\left(x+1\right).
\frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
Kombiner like ledd i x+4-2x-2.
\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)}
Faktoriser x^{2}-2x-3.
\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)}
Hvis du vil legge til eller trekke fra uttrykk, kan du utvide dem for å gjøre nevnerne like. Minste felles multiplum av \left(x-1\right)\left(x+1\right)\left(x+4\right) og \left(x-3\right)\left(x+1\right) er \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right). Multipliser \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} ganger \frac{x-3}{x-3}. Multipliser \frac{1}{\left(x-3\right)\left(x+1\right)} ganger \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-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}
Siden \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)} og \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)} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.
\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)}
Utfør multiplikasjonene i \left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right).
\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}
Kombiner like ledd i -x^{2}+3x+2x-6+x^{2}+4x-x-4.
\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}
Utvid \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right).
Eksempler
Kvadratisk ligning
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometri
4 \sin \theta \cos \theta = 2 \sin \theta
Lineær ligning
y = 3x + 4
Aritmetikk
699 * 533
Matrise
\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]
Samtidig formel
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integrasjon
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Grenser
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