2020 · Q34
What is the value of (a² + ac)/(a²c − c³) − (a² − c²)/(a²c + 2ac² + c³) − 2c/(a² − c²) + 3/(a + c)?
Elementary MathematicsAlgebra
- A0
- B1
- Cac/(a² + c²)
- D6/(a + c)
Explanation
The first term simplifies to a/[c(a-c)] and the second to (a-c)/[c(a+c)]. Combining the first with -2c/[(a-c)(a+c)] gives (a+2c)/[c(a+c)]; subtracting the second leaves 3/[c(a+c)]*c = 3/(a+c), and adding 3/(a+c) yields 6/(a+c). Hence option (D).