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(D) Given equation: $\frac{x+2}{x} + \frac{x}{x+2} = \frac{10}{3}$Taking $LCM$: $\frac{(x+2)^2 + x^2}{x(x+2)} = \frac{10}{3}$Expand the numerator: $\f

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$\{1, -3\}$

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(D) Given equation: $\frac{x+2}{x} + \frac{x}{x+2} = \frac{10}{3}$Taking $LCM$: $\frac{(x+2)^2 + x^2}{x(x+2)} = \frac{10}{3}$Expand the numerator: $\frac{x^2 + 4x + 4 + x^2}{x^2 + 2x} = \frac{10}{3}$$\frac{2x^2 + 4x + 4}{x^2 + 2x} = \frac{10}{3}$Cross-multiply: $3(2x^2 + 4x + 4) = 10(x^2 + 2x)$$6x^2 + 12x + 12 = 10x^2 + 20x$Rearrange terms: $4x^2 + 8x - 12 = 0$Divide by $4$: $x^2 + 2x - 3 = 0$Factorize: $x^2 + 3x - x - 3 = 0$$x(x+3) - 1(x+3) = 0$$(x-1)(x+3) = 0$Thus,$x = 1$ or $x = -3$.The solution set is $\{1, -3\}$.

Solve the following equation using the method of factorization and write its solution set: $\frac{x+2}{x} + \frac{x}{x+2} = \frac{10}{3}$

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