Respuesta :

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[tex]\dfrac{(x+3)^2-(x^2+9)}{2x^2}\\\\use\ (a+b)^2=a^2+2ab+b^2\\\\=\dfrac{x^2+2\cdot x\cdot3+3^2-x^2-9}{2x^2}=\dfrac{x^2-x^2+6x+9-9}{2x^2}\\\\=\dfrac{6x}{2x^2}=\dfrac{3}{x}[/tex]

Answer with explanation:

The correct order of simplifying the expression is:

1. Opening the bracket Using Identity

2. Adding and Subtracting Like terms

The given expression is

[tex]=\frac{(x+3)^2-(x^2+9)}{2x^2}\\\\=\frac{x^2+6 x+9-x^2-9}{2x^2}\\\\=\frac{6x}{2x^2}\\\\=\frac{3}{x}\\\\ \text{Used the identity and law of indices}\\\\(a+b)^2=a^2+2 a b+b^2\\\\ \frac{x^a}{x^b}=x^{a-b}[/tex]

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