Answer:
The given expression is simplified as [tex]\frac{(x+3)^2-(x^2 +9)} {2x^2} = \frac{3}{x}[/tex]
Step-by-step explanation:
Here, the given expression is:
[tex]\frac{(x+3)^2-(x^2 +9)} {2x^2}[/tex]
Now, with ALGEBRAIC IDENTITIES:
[tex](a+b)^2 = a^2 + b^2 + 2ab[/tex]
Now, similarly: [tex](x+3)^2 = x^2 + (3)^2 + 2x(3) = (x^2 + 9 + 6x)[/tex]
Now, substituting the values in the given expression, we get:
[tex]\frac{(x+3)^2-(x^2 +9)} {2x^2} \implies \frac{(x^2 + 9 + 6x)-(x^2 +9)} {2x^2}\\= \frac{(x^2 + 9 + 6x-x^2 -9)} {2x^2} \\= \frac{ 6x} {2x^2} = \frac{3}{x}[/tex]
Hence, the given expression [tex]\frac{(x+3)^2-(x^2 +9)} {2x^2} = \frac{3}{x}[/tex]
