Simplify the Algebraic Expression: (x²-15x)/(3x) Step by Step

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

You can only cancel factors, not terms! The x² is part of a sum (x²-15x), not a standalone factor. You must factor first to separate x as a common factor.

Q: How do I know what to factor out from x²-15x?

Look for the greatest common factor (GCF) of both terms. Both x² and 15x contain x, so factor out x: $ x^2-15x = x(x-15) $

Q: What if there's no common factor to cancel?

Then the fraction is already in simplest form! Not every rational expression can be simplified further. Only cancel when both numerator and denominator share common factors.

Q: Can I cancel the 15 and 3 in the final answer?

No! In $ \frac{x-15}{3} $, the 15 is part of a subtraction (x-15), not a separate factor. You can only cancel factors that multiply the entire numerator or denominator.

Algebraic Simplification with Common Factor Cancellation

Simplify the following expression:

$\frac{x^2-15x}{3x}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:05 Break down the exponent into multiplications

00:10 Mark the common factors

00:25 Take out the common factors from the parentheses

00:31 Reduce what we can

00:37 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:

$\frac{x^2-15x}{3x}$

Step-by-step solution

Let's simplify the given expression:

$\frac{x^2-15x}{3x}$ 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 factoring. First we must determine whether in the numerator we are able to factor out a common term. Following this we must then reduce the possible expressions in the resulting fraction:

$\frac{x^2-15x}{3x} \\ \frac{x(x-15)}{3x} \\ \downarrow\\ \boxed{\frac{x-15}{3} }$ Therefore, the correct answer is answer C.

Final Answer

$\frac{x-15}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Factor numerator and denominator completely before canceling terms
Technique: Factor out x from x²-15x to get x(x-15)
Check: Multiply result by denominator: $\frac{x-15}{3} \cdot 3x = x(x-15) = x^2-15x$ ✓

Common Mistakes

Avoid these frequent errors

Canceling terms without proper factoring
Don't cancel x² and x directly to get x-15/3 = wrong answer! You can only cancel factors, not individual terms within sums or differences. Always factor the numerator completely first: x²-15x = x(x-15), then cancel the common x factor.

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, not terms! The x² is part of a sum (x²-15x), not a standalone factor. You must factor first to separate x as a common factor.

How do I know what to factor out from x²-15x?

Look for the greatest common factor (GCF) of both terms. Both x² and 15x contain x, so factor out x: $x^2-15x = x(x-15)$

What if there's no common factor to cancel?

Then the fraction is already in simplest form! Not every rational expression can be simplified further. Only cancel when both numerator and denominator share common factors.

Can I cancel the 15 and 3 in the final answer?

No! In $\frac{x-15}{3}$ , the 15 is part of a subtraction (x-15), not a separate factor. You can only cancel factors that multiply the entire numerator or denominator.

How do I check if my simplified answer is correct?

Multiply your answer by the original denominator. If you get the original numerator, you're correct! $\frac{x-15}{3} \times 3x = x(x-15) = x^2-15x$ ✓

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