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Reescrevendo o primeiro fator: −3x+152x+16=−3(x+5)2(x+8)\blueE{\dfrac{-3x+15}{2x+16}} =\dfrac{-3(x+5)}{2(x+8)}2x+16−3x+15=2(x+8)−3(x+5)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: x−7x2−25=x−7(x+5)(x−5)\maroonE{\dfrac{x-7}{x^2-25}}=\dfrac{x-7}{(x+5)(x-5)}x2−25x−7=(x+5)(x−5)x−7start 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≠±5x\neq \pm 5x=±5x, does not equal, plus minus, 5 e x≠−8x\neq -8x=−8x, does not equal, minus, 8
Multiplicando e simplificando:
=−3x+152x+16⋅x−7x2−25=−3(x+5)2(x+8)⋅x−7(x+5)(x−5)=−3(x+5)(x−7)2(x+8)(x+5)(x−5)=−3(x−7)2(x+8)(x−5)\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}=2x+16−3x+15⋅x2−25x−7=2(x+8)−3(x+5)⋅(x+5)(x−5)x−7=2(x+8)(x+5)(x−5)−3(x+5)(x−7)=2(x+8)(x−5)−3(x−7)
