Identify Applications of 16 + 8/(2x): Mixed Expression Analysis

Q: Why can't x equal zero in this expression?

When x = 0, the denominator becomes $ 2(0) = 0 $. Division by zero is undefined in mathematics, making the entire expression meaningless.

Q: Does the +16 part affect the domain?

No! The constant term 16 has no restrictions. Only the fractional part $ \frac{8}{2x} $ creates domain limitations because it contains the variable in the denominator.

Q: What if the denominator was 2x + 4 instead?

Then you'd set $ 2x + 4 = 0 $, solve to get $ x = -2 $, and the domain would be all real numbers except -2.

Q: How do I write the domain properly?

Use set notation or inequality notation: $ x \neq 0 $ or "all real numbers except 0". Both express the same restriction clearly.

Q: Can fractions have multiple domain restrictions?

Absolutely! If you have multiple fractions like $ \frac{1}{x} + \frac{2}{x-3} $, then both x ≠ 0 and x ≠ 3 would be restrictions.

Domain Restrictions with Fractional Expressions

Select the field of application of the following fraction:

$16+\frac{8}{2x}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the domain of substitution

00:03 Substitution domain exists, to ensure we don't divide by 0

00:06 Meaning the denominator in the fraction must be different from 0

00:09 We will use this formula in our exercise

00:19 We will isolate X to find the domain of substitution

00:22 This is the domain of substitution

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Select the field of application of the following fraction:

$16+\frac{8}{2x}$

Step-by-step solution

To determine the domain of the expression $16 + \frac{8}{2x}$ , we need to ensure the expression is defined by avoiding division by zero.

The crucial part of this fraction is the denominator, $2x$ . A fraction is undefined when its denominator equals zero. Therefore, we set the denominator equal to zero and solve for $x$ :

Equation: $2x = 0$
Solution: $x = 0$

This means the expression is undefined when $x = 0$ . Hence, the domain of this expression is all real numbers except zero.

So, the domain of the expression is all $x$ such that $x \neq 0$ .

The correct multiple-choice answer is:

$x \neq 0$

Final Answer

$x\neq0$

Key Points to Remember

Essential concepts to master this topic

Domain Rule: Denominators cannot equal zero in any expression
Technique: Set denominator 2x = 0, solve to get x = 0
Check: Verify x ≠ 0 keeps expression defined for all other values ✓

Common Mistakes

Avoid these frequent errors

Only looking at the fraction part
Don't ignore the whole number 16 and focus only on 8/(2x) = wrong domain analysis! The entire expression must be considered together. Always examine every part of the expression to find all restrictions.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

Why can't x equal zero in this expression?

When x = 0, the denominator becomes $2(0) = 0$ . Division by zero is undefined in mathematics, making the entire expression meaningless.

Does the +16 part affect the domain?

No! The constant term 16 has no restrictions. Only the fractional part $\frac{8}{2x}$ creates domain limitations because it contains the variable in the denominator.

What if the denominator was 2x + 4 instead?

Then you'd set $2x + 4 = 0$ , solve to get $x = -2$ , and the domain would be all real numbers except -2.

How do I write the domain properly?

Use set notation or inequality notation: $x \neq 0$ or "all real numbers except 0". Both express the same restriction clearly.

Can fractions have multiple domain restrictions?

Absolutely! If you have multiple fractions like $\frac{1}{x} + \frac{2}{x-3}$ , then both x ≠ 0 and x ≠ 3 would be restrictions.

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Identify Applications of 16 + 8/(2x): Mixed Expression Analysis

Domain Restrictions with Fractional Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't x equal zero in this expression?

Does the +16 part affect the domain?

What if the denominator was 2x + 4 instead?

How do I write the domain properly?

Can fractions have multiple domain restrictions?

🌟 Unlock Your Math Potential

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