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$Perform the operation and express your answer as a single fraction in simplest form. (5)/(2x^(2))-1 Answer:$

Perform the operation and express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{2 x^{2}}-1$ $\newline$ Answer:

Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.

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\frac{5}{2 x^{2}}-1

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Answer:

Identify and Understand Expression: First, we need to identify the expression and understand that we are asked to simplify it. The expression given is $(\frac{5}{2x^{2}})-1$ . We want to express this as a single fraction in simplest form.
Find Common Denominator: To combine the terms into a single fraction, we need a common denominator. The first term has a denominator of $2x^2$ , and the second term, being a whole number, can be thought of as having a denominator of $1$ . To combine them, we can write $-1$ as $-1/1$ and then find a common denominator.
Combine Fractions: The common denominator for $2x^2$ and $1$ is $2x^2$ . We rewrite $-1$ as $-2x^2/2x^2$ to have the same denominator as the first term.
Simplify Numerator: Now we combine the fractions over the common denominator: $\newline$ $(\frac{5}{2x^{2}}) - (\frac{2x^2}{2x^2}) = (\frac{5 - 2x^2}{2x^2})$
Final Single Fraction: We simplify the numerator by subtracting $2x^2$ from $5$ , which gives us: $\newline$ $(\$5 - 2x^2)/(2x^2) = (-2x^2 + 5)/(2x^2)$ \)
Check for Simplification: The expression is now a single fraction and is already in its simplest form. There are no common factors between the numerator and the denominator that can be canceled out.