Problem 80
Question
Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+2}{y}+\frac{y-2}{x}$$
Step-by-Step Solution
Verified Answer
\(\frac{x^2+2x+y^2-2y}{xy}\)
1Step 1: Determine common denominator
The denominators are \(y\) and \(x\). Their least common multiple (LCM) would be their product \(xy\).
2Step 2: Rewrite the fractions with a common denominator
The fractions can now be re-written as \(\frac{(x+2)x}{xy} + \(\frac{(y-2)y}{xy}\). By opening the brackets, we get \(\frac{x^2+2x}{xy} + \(\frac{y^2-2y}{xy}\).
3Step 3: Combine and simplify
The fractions have the common denominator, hence we add them to get \(\frac{x^2+2x+y^2-2y}{xy}\).
Other exercises in this chapter
Problem 80
Explain how to add rational expressions when denominators are opposites. Use an example to support your explanation.
View solution Problem 80
Simplify each rational expression. $$\frac{16-y^{2}}{y(y-8)+16}$$
View solution Problem 80
Find \(b\) so that the solution of \(\frac{7 x+4}{b}+13=x\) is \(-6.\)
View solution Problem 81
Simplify each rational expression. $$\frac{x y+2 y+3 x+6}{x^{2}+5 x+6}$$
View solution