QuestionJune 18, 2025

(2x)/(x+2)-(8)/(x^2)+2x+(3)/(x)

(2x)/(x+2)-(8)/(x^2)+2x+(3)/(x)
(2x)/(x+2)-(8)/(x^2)+2x+(3)/(x)

Solution
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Answer

\frac{2x^2 + 3x - 2}{x(x+2)} Explanation 1. Simplify the expression Factor x^2 + 2x as x(x+2). Rewrite the expression with a common denominator x(x+2). 2. Combine fractions \frac{2x(x)}{x(x+2)} - \frac{8}{x(x+2)} + \frac{3(x+2)}{x(x+2)} = \frac{2x^2 - 8 + 3x + 6}{x(x+2)}. 3. Simplify the numerator Combine like terms in the numerator: 2x^2 + 3x - 2.

Explanation

1. Simplify the expression<br /> Factor $x^2 + 2x$ as $x(x+2)$. Rewrite the expression with a common denominator $x(x+2)$.<br />2. Combine fractions<br /> $\frac{2x(x)}{x(x+2)} - \frac{8}{x(x+2)} + \frac{3(x+2)}{x(x+2)} = \frac{2x^2 - 8 + 3x + 6}{x(x+2)}$.<br />3. Simplify the numerator<br /> Combine like terms in the numerator: $2x^2 + 3x - 2$.
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