Answer:
Explanation:
To find all numbers x that satisfy the equation:
\frac{x+2}{x+1} = \frac{1}{x-1} + 2
x+1
x+2
=
x−1
1
+2
We can simplify and solve the equation step by step:
Step 1: Multiply both sides of the equation by (x+1)(x-1)(x+1)(x−1) to clear the fractions:
(x+2)(x-1) = (x+1) + 2(x-1)(x+2)(x−1)=(x+1)+2(x−1)
Step 2: Expand and simplify:
x^2 + x - 2 = x + 1 + 2x - 2x
2
+x−2=x+1+2x−2
x^2 + x - 2 = 3x - 1x
2
+x−2=3x−1