Answer:
x = -3/2
Step-by-step explanation:
3 / (x − 1) − 1 / (x² − 1) = 5 / (x − 1)
Subtract 3 / (x − 1) from both sides:
-1 / (x² − 1) = 5 / (x − 1) − 3 / (x − 1)
The denominators are the same, so subtract:
-1 / (x² − 1) = 2 / (x − 1)
Cross multiply:
-1 (x − 1) = 2 (x² − 1)
Simplify and solve:
-x + 1 = 2x² − 2
0 = 2x² + x − 3
0 = (x − 1) (2x + 3)
x = -3/2 or 1
x can't be 1 (can't divide by 0), so x = -3/2.
