Ovrednoti
\frac{5+3x-5x^{2}}{x^{2}\left(1-x^{2}\right)}
Odvajajte w.r.t. x
\frac{-10x^{4}+9x^{3}+20x^{2}-3x-10}{x^{3}\left(x^{2}-1\right)^{2}}
Graf
Delež
Kopirano v odložišče
\frac{2}{x\left(x-1\right)}+\frac{5}{\left(-x+1\right)x^{2}}+\frac{3}{x^{2}-1}
Faktorizirajte x^{2}-x. Faktorizirajte x^{2}-x^{3}.
\frac{2x}{\left(x-1\right)x^{2}}+\frac{5\left(-1\right)}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}
Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x\left(x-1\right) in \left(-x+1\right)x^{2} je \left(x-1\right)x^{2}. Pomnožite \frac{2}{x\left(x-1\right)} s/z \frac{x}{x}. Pomnožite \frac{5}{\left(-x+1\right)x^{2}} s/z \frac{-1}{-1}.
\frac{2x+5\left(-1\right)}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}
\frac{2x}{\left(x-1\right)x^{2}} in \frac{5\left(-1\right)}{\left(x-1\right)x^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.
\frac{2x-5}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}
Izvedi množenje v 2x+5\left(-1\right).
\frac{2x-5}{\left(x-1\right)x^{2}}+\frac{3}{\left(x-1\right)\left(x+1\right)}
Faktorizirajte x^{2}-1.
\frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}}+\frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}
Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-1\right)x^{2} in \left(x-1\right)\left(x+1\right) je \left(x-1\right)\left(x+1\right)x^{2}. Pomnožite \frac{2x-5}{\left(x-1\right)x^{2}} s/z \frac{x+1}{x+1}. Pomnožite \frac{3}{\left(x-1\right)\left(x+1\right)} s/z \frac{x^{2}}{x^{2}}.
\frac{\left(2x-5\right)\left(x+1\right)+3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}
\frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}} in \frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.
\frac{2x^{2}+2x-5x-5+3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}
Izvedi množenje v \left(2x-5\right)\left(x+1\right)+3x^{2}.
\frac{5x^{2}-3x-5}{\left(x-1\right)\left(x+1\right)x^{2}}
Združite podobne člene v 2x^{2}+2x-5x-5+3x^{2}.
\frac{5x^{2}-3x-5}{x^{4}-x^{2}}
Razčlenite \left(x-1\right)\left(x+1\right)x^{2}.
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