Respuesta:
1. [tex]\frac{x^2+1}{x+1}[/tex]
2. [tex]=3x^2+10x+32+\frac{87x-37}{x^2-3x+1}[/tex]
Explicación paso a paso:
1. Procedimiento:
[tex]\frac{x^3-x^2+x-1}{x^2-1}\\\\=\frac{\left(x-1\right)\left(x^2+1\right)}{x^2-1}\\\\=\frac{\left(x-1\right)\left(x^2+1\right)}{\left(x+1\right)\left(x-1\right)}\\\\=\frac{x^2+1}{x+1}[/tex]
2. Procedimiento :
[tex]\frac{\left(3x^4+x^3+5x^2+x-5\right)}{\left(x^2-3x+1\right)}\\\\\frac{3x^4+x^3+5x^2+x-5}{x^2-3x+1}=3x^2+\frac{10x^3+2x^2+x-5}{x^2-3x+1}\\\\=3x^2+\frac{10x^3+2x^2+x-5}{x^2-3x+1}\\\\\frac{10x^3+2x^2+x-5}{x^2-3x+1}=10x+\frac{32x^2-9x-5}{x^2-3x+1}\\\\=3x^2+10x+\frac{32x^2-9x-5}{x^2-3x+1}\\\\\frac{32x^2-9x-5}{x^2-3x+1}=32+\frac{87x-37}{x^2-3x+1}\\\\=3x^2+10x+32+\frac{87x-37}{x^2-3x+1}[/tex]
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Verified answer
Respuesta:
1. [tex]\frac{x^2+1}{x+1}[/tex]
2. [tex]=3x^2+10x+32+\frac{87x-37}{x^2-3x+1}[/tex]
Explicación paso a paso:
1. Procedimiento:
[tex]\frac{x^3-x^2+x-1}{x^2-1}\\\\=\frac{\left(x-1\right)\left(x^2+1\right)}{x^2-1}\\\\=\frac{\left(x-1\right)\left(x^2+1\right)}{\left(x+1\right)\left(x-1\right)}\\\\=\frac{x^2+1}{x+1}[/tex]
2. Procedimiento :
[tex]\frac{\left(3x^4+x^3+5x^2+x-5\right)}{\left(x^2-3x+1\right)}\\\\\frac{3x^4+x^3+5x^2+x-5}{x^2-3x+1}=3x^2+\frac{10x^3+2x^2+x-5}{x^2-3x+1}\\\\=3x^2+\frac{10x^3+2x^2+x-5}{x^2-3x+1}\\\\\frac{10x^3+2x^2+x-5}{x^2-3x+1}=10x+\frac{32x^2-9x-5}{x^2-3x+1}\\\\=3x^2+10x+\frac{32x^2-9x-5}{x^2-3x+1}\\\\\frac{32x^2-9x-5}{x^2-3x+1}=32+\frac{87x-37}{x^2-3x+1}\\\\=3x^2+10x+32+\frac{87x-37}{x^2-3x+1}[/tex]