Carcass wrote:
What is the value of a if \(\frac{a+1}{a-3} - \frac{a+2}{a-4} = 0\) ?
A. -2
B. -1
C. 0
D. 1
E. 2
Kudos for the right answer and explanation
Given: \(\frac{a+1}{a-3} - \frac{a+2}{a-4} = 0\)
Add \(\frac{a+2}{a-4}\) to both sides of the equation to get: \(\frac{a+1}{a-3} = \frac{a+2}{a-4}\)
Cross multiply to get: \((a+1)(a-4)=(a-3)(a+2)\)
Use F.O.I.L. to expand and simplify both sides: \(a^2-3a-4=a^2-a-6\)
Subtract \(a^2\) both sides: \(-3a-4=-a-6\)
Add \(3a\) both sides: \(-4=2a-6\)
Add \(6\) both sides: \(2=2a\)
Solve: \(a = 1\)
Answer: D
Cheers,
Brent