Simplify the Algebraic Fraction: (x²-24x)÷8x Step by Step

Q: Why can't I just cancel the x² with the x in the denominator?

You can only cancel factors (terms being multiplied), not individual terms being added or subtracted. The x² and -24x are added together, so you must factor first to create multiplication before canceling.

Q: How do I know what to factor out from the numerator?

Look for the greatest common factor (GCF) of all terms. Here, both x² and 24x contain x as a factor, so factor out x: $ x^2-24x = x(x-24) $

Q: Can I simplify this fraction further?

The answer $ \frac{x-24}{8} $ is in simplest form because x-24 and 8 share no common factors. The expression cannot be reduced any further.

Q: How do I check if my factoring is correct?

Expand your factored form to see if you get back the original! Here: $ x(x-24) = x^2 - 24x $ ✓ This matches our original numerator.

Algebraic Fraction Simplification with Factorization

Simplify the following expression:

$\frac{x^2-24x}{8x}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:04 Let's break down the exponent into multiples

00:12 Let's mark the common factors

00:26 Let's take out the common factors from the parentheses

00:35 Let's reduce what we can

00:42 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

Simplify the following expression:

$\frac{x^2-24x}{8x}$

Step-by-step solution

Let's simplify the given expression:

$\frac{x^2-24x}{8x}$ Remember that we can reduce complete expressions only when both the numerator and denominator are completely factored into multiplication expressions,

For this, we'll use factorization. First we must identify that in the numerator we can factor out a common term. Following this we will then proceed to reduce the possible expressions in the resulting fraction:

$\frac{x^2-24x}{8x} \\ \frac{x(x-24)}{8x} \\ \downarrow\\ \boxed{\frac{x-24}{8} }$ Therefore, the correct answer is answer A.

Final Answer

$\frac{x-24}{8}$

Key Points to Remember

Essential concepts to master this topic

Factoring Rule: Factor numerator completely before canceling common terms
Technique: Factor out x from x²-24x to get x(x-24)
Check: Verify x≠0: substitute x=8 gives (8-24)/8 = -16/8 = -2 ✓

Common Mistakes

Avoid these frequent errors

Canceling terms instead of factors
Don't cancel individual terms like canceling x² with x = wrong simplification! Terms can only be canceled when they appear as factors (multiplication). Always factor the numerator completely first, then cancel common factors.

Practice Quiz

Test your knowledge with interactive questions

Identify the field of application of the following fraction:

$\frac{7}{13+x}$

FAQ

Everything you need to know about this question

Why can't I just cancel the x² with the x in the denominator?

You can only cancel factors (terms being multiplied), not individual terms being added or subtracted. The x² and -24x are added together, so you must factor first to create multiplication before canceling.

How do I know what to factor out from the numerator?

Look for the greatest common factor (GCF) of all terms. Here, both x² and 24x contain x as a factor, so factor out x: $x^2-24x = x(x-24)$

What if x equals zero in this problem?

Great question! When x = 0, the original expression becomes $\frac{0}{0}$ which is undefined. So our answer $\frac{x-24}{8}$ is valid for all real numbers except x = 0.

Can I simplify this fraction further?

The answer $\frac{x-24}{8}$ is in simplest form because x-24 and 8 share no common factors. The expression cannot be reduced any further.

How do I check if my factoring is correct?

Expand your factored form to see if you get back the original! Here: $x(x-24) = x^2 - 24x$ ✓ This matches our original numerator.

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