Factoring Algebraic Expressions with Fractional Exponents

In summary, the problem is to simplify the expression (4x-1)^{1/2}-1/3(4x-1)^{3/2}. The correct answer is (4x-1)^{1/2}(x-1), but the answer in the book is incorrect. The suggested method of checking the solutions by plugging in a value for x and solving with a calculator confirms that the book's answer is wrong.
  • #1

Homework Statement



[tex](4x-1)^{1/2}-1/3(4x-1)^{3/2}[/tex]

Homework Equations


The Attempt at a Solution



I think the GCF is [tex](4x-1)^{1/2}[/tex]. So, I get [tex](4x-1)^{1/2}(1+(-1/3(4x-1)))[/tex] = [tex](4x-1)^{1/2}(-4/3x+4/3)[/tex] = [tex]-4/3(4x-1)^{1/2}(x-1)[/tex]

However, the answer in the book is [tex]4/3(4x-1)^{1/2}(x-1)[/tex]. I've done it several ways, and I either get a minus sign on the [tex]4/3[/tex], or the [tex](x-1)[/tex] becomes [tex](x+1)[/tex].

What am I missing?
 
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  • #2
If the problem you've listed is the same as the problem in your book, then you're right and the answer in your book is wrong.
 
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  • #3
You can also check your work versus the book answer by plugging in a number for x, and solving the original expression and your final expression with a calculator. What answers do you get, for example, for x = 2?
 
  • #4
Thanks folks! I did try inputting a value for x, but I was still put off by the book's answer. I just wanted to verify from those more knowledgeable than I.

Thanks!
 

What is factoring algebraic expressions with fractional exponents?

Factoring algebraic expressions with fractional exponents involves finding the common factors in an expression that contains variables raised to fractional powers. This process helps simplify the expression and solve equations more easily.

How do I factor an expression with fractional exponents?

To factor an expression with fractional exponents, identify the common factors in the numerator and denominator of each term. Then, use the properties of exponents to rewrite the expression in its simplest form.

Why is factoring algebraic expressions with fractional exponents important?

Factoring algebraic expressions with fractional exponents is important because it helps us solve equations, simplify expressions, and find equivalent forms of expressions. It also allows us to better understand the relationships between different terms in an expression.

Can I factor an expression with fractional exponents using the distributive property?

Yes, the distributive property can be used to factor an expression with fractional exponents. However, it may not always be the most efficient method, as there are other strategies specifically designed for factoring expressions with fractional exponents.

What are some common mistakes to avoid when factoring algebraic expressions with fractional exponents?

Some common mistakes to avoid when factoring algebraic expressions with fractional exponents include forgetting to apply the properties of exponents, overlooking common factors, and not simplifying the expression completely. It is also important to pay attention to the signs and coefficients when factoring expressions with fractional exponents.

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