Question

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

Answer 1

It is A

Explanation:

edge 2020

Answer 2

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

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}  = (3)/(x)`

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