Respuesta:
Explicación paso a paso:
14.
[tex]x^{2} -5x-\frac{3x(x+2)}{x-2}\\\frac{x^{2} (x-2)-5x(x-2)-3x(x+2)}{x-2} \\\frac{x^{3} -2x^{2} -5x^{2} +10x-3x^{2} -6x}{x-2} \\\frac{x^{3}-10x^{2} +4x }{x-2} \\\frac{x(x^{2} -10x+4)}{x-2} \\\\[/tex]
16.
[tex]\frac{x^{3}+2 }{x^{2} -x+1} -(x+1)\\\frac{x^{3}+2-(x+1)(x^{2} -x+1) }{x^{2} -x+1} \\\frac{x^{3}+2-x^{3}+x^{2} -x-x^{2} +x-1 }{x^{2} -x+1} \\\frac{1}{x^{2} -x+1}[/tex]
18.
[tex]3a+\frac{3a^{2}b+3ab^{2} }{a^{2}-b^{2} } \\\frac{3a^{3}-3ab^{2}+3a^{2}b+3ab^{2}}{a^{2}-b^{2}} \\\frac{3a^{3} +3a^{2} b}{a^{2}-b^{2}} \\\frac{3a^{2} (a+b)}{(a+b)(a-b)} \\\frac{3a^{2} }{a-b}[/tex]
20.
[tex]a^{2} -3a+5+\frac{2a^{3}-11a+9 }{a^{2}+a-2 } \\\frac{(a^{2}+1 )(a+1)(a-1)}{(a+2)(a-1)} \\\frac{(a^{2}+1)(a+1)}{a+2}[/tex]
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Verified answer
Respuesta:
Explicación paso a paso:
14.
[tex]x^{2} -5x-\frac{3x(x+2)}{x-2}\\\frac{x^{2} (x-2)-5x(x-2)-3x(x+2)}{x-2} \\\frac{x^{3} -2x^{2} -5x^{2} +10x-3x^{2} -6x}{x-2} \\\frac{x^{3}-10x^{2} +4x }{x-2} \\\frac{x(x^{2} -10x+4)}{x-2} \\\\[/tex]
16.
[tex]\frac{x^{3}+2 }{x^{2} -x+1} -(x+1)\\\frac{x^{3}+2-(x+1)(x^{2} -x+1) }{x^{2} -x+1} \\\frac{x^{3}+2-x^{3}+x^{2} -x-x^{2} +x-1 }{x^{2} -x+1} \\\frac{1}{x^{2} -x+1}[/tex]
18.
[tex]3a+\frac{3a^{2}b+3ab^{2} }{a^{2}-b^{2} } \\\frac{3a^{3}-3ab^{2}+3a^{2}b+3ab^{2}}{a^{2}-b^{2}} \\\frac{3a^{3} +3a^{2} b}{a^{2}-b^{2}} \\\frac{3a^{2} (a+b)}{(a+b)(a-b)} \\\frac{3a^{2} }{a-b}[/tex]
20.
[tex]a^{2} -3a+5+\frac{2a^{3}-11a+9 }{a^{2}+a-2 } \\\frac{(a^{2}+1 )(a+1)(a-1)}{(a+2)(a-1)} \\\frac{(a^{2}+1)(a+1)}{a+2}[/tex]