Question

What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2?

Answer 1

Answer:

The given expression is simplified as $\frac{(x+3)^2-(x^2 +9)} {2x^2} = \frac{3}{x}$

Step-by-step explanation:

Here, the given expression is:

$\frac{(x+3)^2-(x^2 +9)} {2x^2}$

Now, with ALGEBRAIC IDENTITIES:

$(a+b)^2 = a^2 + b^2 + 2ab$

Now, similarly: $(x+3)^2 = x^2 + (3)^2 + 2x(3) = (x^2 + 9 + 6x)$

Now, substituting the values in the given expression, we get:

$\frac{(x+3)^2-(x^2 +9)} {2x^2} \implies \frac{(x^2 + 9 + 6x)-(x^2 +9)} {2x^2}\\= \frac{(x^2 + 9 + 6x-x^2 -9)} {2x^2} \\= \frac{ 6x} {2x^2} = \frac{3}{x}$

Hence, the given expression $\frac{(x+3)^2-(x^2 +9)} {2x^2} = \frac{3}{x}$