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Chapter 0: Problem 63

Simplify each complex rational expression. $$\frac{\frac{1}{x}+\frac{1}{y}}{x+y}$$

Short Answer

Expert verified
The simplified form of the complex rational expression given is \(1/xy\).

Step by step solution

01

Find the Common Denominator in the Numerator

For the rational expressions \(1/x\) and \(1/y\) in the numerator, the common denominator is \(xy\). Let's re-write these fractions with the common denominator.
02

Simplify the Numerator

Now that the two fractions in the numerator have a common denominator \(xy\), we combine them by adding their numerators. So, \((1/x) + (1/y)\) becomes \((y + x)/xy\).
03

Replace the Numerator

Now replace the numerator of the original complex fraction with the simplified version we obtained in Step 2. So, the original complex fraction becomes \((y + x)/(xy(x + y))\).
04

Simplify the Complex Fraction

The above fraction simplifies to \(1/xy\) by cancelling out the \((x + y)\) in the numerator and denominator.

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Most popular questions from this chapter

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{x^{2}-25}{x-5}=x-5$$

Explain how to multiply rational expressions.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\).

Explain how to divide rational expressions.
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