Ola. Como simplifico as expressões algébricas das seguintes situações:
a) x²-xy+3x-3y
xy+3y
b) 6x³+28x²-10x
12x³-4x²
c) x³-16x
x²-4
Soluções para a tarefa
Respondido por
2
Boa tarde Renata!
Solução!
![a)\\\\
\dfrac{ x^{2} -xy+3x-3y}{xy+3y}\\\\\\
\dfrac{ x^{2}+3x -xy-3y}{xy+3y}\\\\\\
\dfrac{ x(x+3) -y(x+3)}{y(x+3)}\\\\\\
\dfrac{(x+3)[( x -y)]}{y(x+3)}\\\\\\
\dfrac{x-y}{y}\\\\\\
\boxed{Resposta:\dfrac{x-y}{y}}](https://tex.z-dn.net/?f=a%29%5C%5C%5C%5C%0A+%0A+%5Cdfrac%7B+x%5E%7B2%7D+-xy%2B3x-3y%7D%7Bxy%2B3y%7D%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B+x%5E%7B2%7D%2B3x+-xy-3y%7D%7Bxy%2B3y%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7B+x%28x%2B3%29+-y%28x%2B3%29%7D%7By%28x%2B3%29%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7B%28x%2B3%29%5B%28+x+-y%29%5D%7D%7By%28x%2B3%29%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7Bx-y%7D%7By%7D%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A%5Cdfrac%7Bx-y%7D%7By%7D%7D%0A%0A "a)\\\\
\dfrac{ x^{2} -xy+3x-3y}{xy+3y}\\\\\\
\dfrac{ x^{2}+3x -xy-3y}{xy+3y}\\\\\\
\dfrac{ x(x+3) -y(x+3)}{y(x+3)}\\\\\\
\dfrac{(x+3)[( x -y)]}{y(x+3)}\\\\\\
\dfrac{x-y}{y}\\\\\\
\boxed{Resposta:\dfrac{x-y}{y}}")
![b)\\\\
\dfrac{6 x^{3}+28 x^{2} -10x }{12 x^{3}-4 x^{2}}\\\\\\
\dfrac{2x[(3 x^{2}+14x -5)] }{2x[(6 x^{2}-2x)]}}\\\\\\
\dfrac{(3 x^{2}+14x -5) }{(6 x^{2}-2x)}}\\\\\\
\dfrac{(x+5)(x- \frac{1}{3}) }{(x+0)(x- \frac{1}{3}) }}\\\\\\
\dfrac{x+5 }{x}}\\\\\\
\boxed{Resposta:\dfrac{x+5 }{x}}}](https://tex.z-dn.net/?f=b%29%5C%5C%5C%5C%0A+%5Cdfrac%7B6+x%5E%7B3%7D%2B28+x%5E%7B2%7D+-10x+%7D%7B12+x%5E%7B3%7D-4+x%5E%7B2%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7B2x%5B%283+x%5E%7B2%7D%2B14x+-5%29%5D+%7D%7B2x%5B%286+x%5E%7B2%7D-2x%29%5D%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7B%283+x%5E%7B2%7D%2B14x+-5%29+%7D%7B%286+x%5E%7B2%7D-2x%29%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7B%28x%2B5%29%28x-+%5Cfrac%7B1%7D%7B3%7D%29++%7D%7B%28x%2B0%29%28x-+%5Cfrac%7B1%7D%7B3%7D%29+%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7Bx%2B5+%7D%7Bx%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A%5Cdfrac%7Bx%2B5+%7D%7Bx%7D%7D%7D%0A "b)\\\\
\dfrac{6 x^{3}+28 x^{2} -10x }{12 x^{3}-4 x^{2}}\\\\\\
\dfrac{2x[(3 x^{2}+14x -5)] }{2x[(6 x^{2}-2x)]}}\\\\\\
\dfrac{(3 x^{2}+14x -5) }{(6 x^{2}-2x)}}\\\\\\
\dfrac{(x+5)(x- \frac{1}{3}) }{(x+0)(x- \frac{1}{3}) }}\\\\\\
\dfrac{x+5 }{x}}\\\\\\
\boxed{Resposta:\dfrac{x+5 }{x}}}")
Essa quetão acima pode ser simplificada diretamente usando o algoritmo de Briot Ruffini.
Ou você pode usar a extensão de Galois que resolve equações só ate o terceiro. grau.
![c)\\\\
\dfrac{ x^{3} -16x}{ x^{2} -4}\\\\\\\
\dfrac{x( x^{2} -16)}{ x^{2} -4}\\\\\\\
\dfrac{x(x+4)(x-4)}{(x+2)(x-2)}\\\\\\\
Resposta: Nao~~da~~para~~simplificar.](https://tex.z-dn.net/?f=c%29%5C%5C%5C%5C%0A+%5Cdfrac%7B+x%5E%7B3%7D+-16x%7D%7B+x%5E%7B2%7D+-4%7D%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7Bx%28+x%5E%7B2%7D+-16%29%7D%7B+x%5E%7B2%7D+-4%7D%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7Bx%28x%2B4%29%28x-4%29%7D%7B%28x%2B2%29%28x-2%29%7D%5C%5C%5C%5C%5C%5C%5C%0AResposta%3A+Nao%7E%7Eda%7E%7Epara%7E%7Esimplificar.%0A+++ "c)\\\\
\dfrac{ x^{3} -16x}{ x^{2} -4}\\\\\\\
\dfrac{x( x^{2} -16)}{ x^{2} -4}\\\\\\\
\dfrac{x(x+4)(x-4)}{(x+2)(x-2)}\\\\\\\
Resposta: Nao~~da~~para~~simplificar.")
Boa tarde!
Bons estudos!
Solução!
Essa quetão acima pode ser simplificada diretamente usando o algoritmo de Briot Ruffini.
Ou você pode usar a extensão de Galois que resolve equações só ate o terceiro. grau.
Boa tarde!
Bons estudos!
Respondido por
0
b) 6x³+28x²-10x
12x³-4x²
x³+7x²-10x
6x³-x²
12x³-4x²
x³+7x²-10x
6x³-x²
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