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Chapter 0: Problem 96

Factor and simplify each algebraic expression. $$12 x^{-\frac{3}{4}}+6 x^{\frac{1}{4}}$$

Short Answer

Expert verified
\[6x^{-\frac{3}{4}}(2+x)\]

Step by step solution

01

Identifying common factors

In the expression \(12 x^{-\frac{3}{4}}+6 x^{\frac{1}{4}}\), we start by identifying the common factors which include the numeric part and the variable part. The common numeric factor is 6 and the common variable factor is \(x^{-\frac{3}{4}}\) which is smallest power of x.
02

Factor out the common factors

Now, factor out the common factors from each term of the expression which gives us: \[6x^{-\frac{3}{4}}(2+x)\]
03

Simplify

We already factored out the greatest common factor in the previous step. So, there is no simplification required in this case. Therefore, the expression remains the same: \[6x^{-\frac{3}{4}}(2+x)\]

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Most popular questions from this chapter

Factor completely. $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$

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