Sure, let's break down the function \( f(x) = x^2 + \frac{x}{x} - 3 \times 153 \) step-by-step:
1. Identify each term in the function:
- The first term is \( x^2 \), which represents \( x \) squared.
- The second term is \( \frac{x}{x} \). Since \( x \) divided by \( x \) is 1 (for \( x \neq 0 \)), this term simplifies to 1.
- The third term is \( -3 \times 153 \). This represents \(-3\) times 153.
2. Simplify each term where possible:
- \( x^2 \) remains as it is.
- \( \frac{x}{x} = 1 \) (for \( x \neq 0 \)).
- \( -3 \times 153 \) simplifies to \( -459 \) (since \( 3 \times 153 = 459 \)).
3. Combine all the simplified terms:
[tex]\[
f(x) = x^2 + 1 - 459
\][/tex]
4. Simplify the function further by combining the constants:
[tex]\[
1 - 459 = -458
\][/tex]
So, the function simplifies to:
[tex]\[
f(x) = x^2 - 458
\][/tex]
Therefore, the simplified form of the function \( f(x) \) is:
[tex]\[
f(x) = x^2 - 458
\][/tex]
