Pergunta

1)) Simplify.Express your answer as a single fraction in simplest form. (3d)/(d+2)-(3d-4) square
Solução

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NúbiaVeterano · Tutor por 11 anos
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To simplify the expression \(\frac{3d}{d+2} - (3d - 4)\), we need to combine the terms into a single fraction.<br /><br />First, rewrite the expression:<br />\[<br />\frac{3d}{d+2} - (3d - 4)<br />\]<br /><br />Next, find a common denominator for the terms. The common denominator is \(d+2\).<br /><br />Rewrite the second term with the common denominator:<br />\[<br />\frac{3d}{d+2} - \frac{(3d - 4)(d+2)}{d+2}<br />\]<br /><br />Now, distribute in the numerator of the second term:<br />\[<br />\frac{3d}{d+2} - \frac{3d(d+2) - 4(d+2)}{d+2}<br />\]<br /><br />Simplify the numerator of the second term:<br />\[<br />3d(d+2) - 4(d+2) = 3d^2 + 6d - 4d - 8 = 3d^2 + 2d - 8<br />\]<br /><br />So the expression becomes:<br />\[<br />\frac{3d}{d+2} - \frac{3d^2 + 2d - 8}{d+2}<br />\]<br /><br />Combine the fractions over the common denominator:<br />\[<br />\frac{3d - (3d^2 + 2d - 8)}{d+2}<br />\]<br /><br />Simplify the numerator:<br />\[<br />3d - 3d^2 - 2d + 8 = -3d^2 + d + 8<br />\]<br /><br />Thus, the simplified expression is:<br />\[<br />\frac{-3d^2 + d + 8}{d+2}<br />\]<br /><br />Therefore, the final answer is:<br />\[<br />\boxed{\frac{-3d^2 + d + 8}{d+2}}<br />\]
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