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

User Janjust
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2 Answers

1 vote

Answer:

It is A

Explanation:

edge 2020

User Busticated
by
8.0k points
3 votes

Answer:

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)

User Tom Juergens
by
8.6k points

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