I-evaluate
-\frac{x^{3}+x^{2}+x+1}{x^{2}+2x-1}
Palawakin
-\frac{x^{3}+x^{2}+x+1}{x^{2}+2x-1}
Graph
Ibahagi
Kinopya sa clipboard
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-x
I-factor out ang x^{2}+2x-1.
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-\frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. I-multiply ang x times \frac{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}.
\frac{x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Dahil may parehong denominator ang \frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)} at \frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.
\frac{x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Gawin ang mga pag-multiply sa x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right).
\frac{-x^{2}-x-1-x^{3}}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Pagsamahin ang magkakatulad na term sa x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x.
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-\left(\sqrt{2}\right)^{2}+1}
Palawakin ang \left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right).
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-2+1}
Ang square ng \sqrt{2} ay 2.
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-1}
Idagdag ang -2 at 1 para makuha ang -1.
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-x
I-factor out ang x^{2}+2x-1.
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-\frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. I-multiply ang x times \frac{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}.
\frac{x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Dahil may parehong denominator ang \frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)} at \frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.
\frac{x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Gawin ang mga pag-multiply sa x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right).
\frac{-x^{2}-x-1-x^{3}}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
Pagsamahin ang magkakatulad na term sa x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x.
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-\left(\sqrt{2}\right)^{2}+1}
Palawakin ang \left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right).
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-2+1}
Ang square ng \sqrt{2} ay 2.
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-1}
Idagdag ang -2 at 1 para makuha ang -1.
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