Simplify the Expression: (5x²-15x)/(x-3) Step-by-Step

Q: Why can't I just cancel the x terms directly?

You can only cancel factors (things being multiplied), not terms (things being added or subtracted). The numerator $ 5x^2-15x $ must be factored first!

Q: What if x equals 3 in my answer?

Great question! When x = 3, the original expression is undefined because we'd divide by zero. So x ≠ 3 is a restriction on our simplified answer $ 5x $.

Q: How do I know what to factor out?

Look for the greatest common factor (GCF) of all terms. Here, both $ 5x^2 $ and $ 15x $ contain 5x, so factor that out first.

Rational Expression Simplification with Factoring

Simplify the following expression:

$\frac{5x^2-15x}{x-3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:05 Break down the power into products

00:15 Mark the common factors

00:21 Take out the common factors from the parentheses

00:31 Reduce what's possible

00:35 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:

$\frac{5x^2-15x}{x-3}$

Step-by-step solution

Let's simplify the given expression:

$\frac{5x^2-15x}{x-3}$ 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. We must first identify that in the numerator we can factor out a common term, then we proceed to reduce the expressions in the obtained fraction (reduction sign):

$\frac{5x^2-15x}{x-3} \\ \frac{5x(x-3)}{x-3} \\ \downarrow\\ \boxed{5x}$ Therefore, the correct answer is answer B.

Final Answer

$5x$

Key Points to Remember

Essential concepts to master this topic

Rule: Factor completely before reducing any common factors
Technique: Factor out 5x from numerator: 5x(x-3)
Check: Substitute x=2: 5(2)=10 and original equals 20/(-1)=-20 ✓

Common Mistakes

Avoid these frequent errors

Canceling terms instead of factors
Don't cancel individual terms like canceling x² with x = wrong simplification! This breaks mathematical rules and gives incorrect answers. Always factor completely first, then cancel only common factors from numerator and denominator.

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 I just cancel the x terms directly?

You can only cancel factors (things being multiplied), not terms (things being added or subtracted). The numerator $5x^2-15x$ must be factored first!

What if x equals 3 in my answer?

Great question! When x = 3, the original expression is undefined because we'd divide by zero. So x ≠ 3 is a restriction on our simplified answer $5x$ .

How do I know what to factor out?

Look for the greatest common factor (GCF) of all terms. Here, both $5x^2$ and $15x$ contain 5x, so factor that out first.

Can I check my answer by plugging in numbers?

Yes! Pick any value except x = 3, substitute into both the original and simplified expressions. If they give the same result, you're correct!

What if the denominator doesn't factor out completely?

That's fine! Sometimes after factoring the numerator, you'll still have terms left over. The key is finding common factors between numerator and denominator to cancel.

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