Simplify the Expression: 5x²/(3y·20x) Step-by-Step Solution

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

You can only cancel identical factors, not different powers! $ x^2 = x \times x $, so you can cancel one x factor, leaving one x in the numerator.

Q: How do I know which factors I can cancel?

Look for exact matches between numerator and denominator. In this problem, both have the factor 5x, so that's what you cancel - not just 5 or just x separately.

Q: What if there are no common factors to cancel?

Then the fraction is already in simplest form! Just multiply out the denominator terms like $ 3y \times 20x = 60xy $ and leave it as is.

Q: Should I multiply out 3y×4 in the final answer?

Yes! Always simplify arithmetic in the final step. $ 3 \times 4 = 12 $, giving you the clean answer $ \frac{x}{12y} $.

Q: Can I cancel variables that appear in different terms?

No! You can only cancel factors that multiply the entire numerator or denominator. Terms that are added or subtracted cannot be canceled.

Rational Expression Simplification with Variable Cancellation

$5x^2/(3y\cdot20x)=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's write division as a fraction

00:12 Let's break X squared into its multiplication with itself

00:20 Let's factorize 20 into factors 5 and 4

00:30 Let's reduce what we can

00:42 Let's calculate 3 times 4

00:48 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

$5x^2/(3y\cdot20x)=\text{?}$

Step-by-step solution

Let's write the exercise as a fraction:

$\frac{5x^2}{3y\times20x}=$

We'll factor the numerator of the fraction into a multiplication exercise:

$\frac{5x\times x}{3y\times20x}=$

Let's write the 20 in the denominator of the fraction as a smaller multiplication exercise:

$\frac{5x\times x}{3y\times4\times5x}=$

We'll cancel out the 5x in both the numerator and denominator of the fraction:

$\frac{x}{3y\times4}=$

Let's multiply the denominator of the fraction:

$\frac{x}{12y}$

Final Answer

$\frac{x}{12y}$

Key Points to Remember

Essential concepts to master this topic

Rule: Cancel common factors from numerator and denominator carefully
Technique: Factor completely: $\frac{5x \times x}{3y \times 4 \times 5x}$ then cancel 5x
Check: Substitute values to verify $\frac{x}{12y}$ matches original expression ✓

Common Mistakes

Avoid these frequent errors

Canceling terms instead of factors
Don't cancel x from 5x² and 20x directly = wrong simplification! You must factor completely first, then cancel identical factors. Always factor expressions like 5x² = 5x·x and 20x = 4·5·x before canceling.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

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 identical factors, not different powers! $x^2 = x \times x$ , so you can cancel one x factor, leaving one x in the numerator.

How do I know which factors I can cancel?

Look for exact matches between numerator and denominator. In this problem, both have the factor 5x, so that's what you cancel - not just 5 or just x separately.

What if there are no common factors to cancel?

Then the fraction is already in simplest form! Just multiply out the denominator terms like $3y \times 20x = 60xy$ and leave it as is.

Should I multiply out 3y×4 in the final answer?

Yes! Always simplify arithmetic in the final step. $3 \times 4 = 12$ , giving you the clean answer $\frac{x}{12y}$ .

Can I cancel variables that appear in different terms?

No! You can only cancel factors that multiply the entire numerator or denominator. Terms that are added or subtracted cannot be canceled.

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Simplify the Expression: 5x²/(3y·20x) Step-by-Step Solution

Rational Expression Simplification with Variable Cancellation

❤️ 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 I just cancel the x² with the x in the denominator?

How do I know which factors I can cancel?

What if there are no common factors to cancel?

Should I multiply out 3y×4 in the final answer?

Can I cancel variables that appear in different terms?

🌟 Unlock Your Math Potential

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