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Conteúdo principal

Multiplique e divida expressões racionais: análise de erros

Problema

Roberto tentou realizar a seguinte multiplicação e simplificá-la:
start color #0c7f99, start fraction, minus, 3, x, plus, 15, divided by, 2, x, plus, 16, end fraction, end color #0c7f99, dot, start color #9e034e, start fraction, x, minus, 7, divided by, x, squared, minus, 25, end fraction, end color #9e034e
Veja abaixo o trabalho dele:
Reescrevendo o primeiro fator: start color #0c7f99, start fraction, minus, 3, x, plus, 15, divided by, 2, x, plus, 16, end fraction, end color #0c7f99, equals, start fraction, minus, 3, left parenthesis, x, plus, 5, right parenthesis, divided by, 2, left parenthesis, x, plus, 8, right parenthesis, end fraction
Reescrevendo o segundo fator: start color #9e034e, start fraction, x, minus, 7, divided by, x, squared, minus, 25, end fraction, end color #9e034e, equals, start fraction, x, minus, 7, divided by, left parenthesis, x, plus, 5, right parenthesis, left parenthesis, x, minus, 5, right parenthesis, end fraction
Encontrando os valores excluídos: x, does not equal, plus minus, 5 e x, does not equal, minus, 8
Multiplicando e simplificando:
=3x+152x+16x7x225=3(x+5)2(x+8)x7(x+5)(x5)=3(x+5)(x7)2(x+8)(x+5)(x5)=3(x7)2(x+8)(x5)\begin{aligned} &\phantom{=}\blueE{\dfrac{-3x+15}{2x+16}} \cdot \maroonE{\dfrac{x-7}{x^2-25}} \\\\ &=\dfrac{-3(x+5)}{2(x+8)}\cdot\dfrac{x-7}{(x+5)(x-5)} \\\\ &=\dfrac{-3\cancel{(x+5)}(x-7)}{2(x+8)\cancel{(x+5)}(x-5)} \\\\ &=\dfrac{-3(x-7)}{2(x+8)(x-5)} \end{aligned}
Que erro Roberto cometeu?
Escolha 1 resposta: