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Chapter 7: Problem 8

Find the least common denominator of the rational expressions. $$\frac{8}{11(y+5)} \text { and } \frac{12}{y}$$

Short Answer

Expert verified
The least common denominator of the given rational expressions is \(11y(y+5)\).

Step by step solution

01

Identifying the Denominators

The denominators of the two given rational expressions are \(11(y+5)\) and \(y\). We need these for comparison.
02

Factorizing the Denominators

For the denominator \(11(y+5)\), there are no more prime factors other than 11 and \(y+5\). For the denominator \(y\), it is already a prime number and hence can't be factorized further.
03

Determining the LCD

The LCD can be found by multiplying each factor the greatest number of times it occurs in either of the denominators. So, the LCD of \(11(y+5)\) and \(y\) would be \(11y(y+5)\).

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3 x}{x^{2}-y^{2}}-\frac{2}{y-x}$$

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. The reason I can rewrite rational expressions with a common denominator is that 1 is the multiplicative identity.

Factor: $$6 x^{3}-6 x^{2}-120 x$$

Exercises \(123-125\) will help you prepare for the material covered in the next section. Multiply and simplify: \(\quad x y\left(\frac{1}{x}+\frac{1}{y}\right)\)

Graph: \(3 x-y=3\).
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