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Chapter 7: Problem 2

Find the least common denominator of the rational expressions. $$\frac{11}{25 x^{2}} \text { and } \frac{17}{35 x}$$

Short Answer

Expert verified
The least common denominator between the given fractions is \(175x^{2}\).

Step by step solution

01

Identify the Denominators

The denominators of the given fractions are \(25x^{2}\) and \(35x\). This you can observe directly from the problem statement.
02

Prime Factorization

In this step you need to find the prime factorizations of each part of your denominators. The prime factorization of 25 is \(5^{2}\), of 35 is \(5 \times 7\), \(x^{2}\) is the prime factorization of the first \(x^{2}\), and for the last \(x\) it's \(x\).
03

Least Common Multiple (LCM)

The LCM is found by multiplying the highest power of all primes numbers gotten from the fractions. That means: \(5^{2}\), 7 and \(x^{2}\) are all included in the LCM. So, the LCM of \(25x^{2}\) and \(35x\) is \(5^{2} \times 7 \times x^{2}\), which simplifies to \(175 x^{2}\).

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x}+9$$

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