SOLUTION: solve the following equations. 1. 1/(x-2)^2 + 1/(x-2) -6 =0 2. 2/(x+1)

Click here to see ALL problems on Quadratic Equations

Question 498166: solve the following equations.
1. 1/(x-2)^2 + 1/(x-2) -6 =0
2. 2/(x+1) - 5/(sqrt x+1) +3 =0
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
solve the following equations.
1. 1/(x-2)^2 + 1/(x-2) -6 =0
2. 2/(x+1) - 5/(sqrt x+1) +3 =0
**
1. 1/(x-2)^2 + 1/(x-2) -6 =0
let u=1/(x-2)
u^2=1/(x-2)^2
u^2+u-6=0
(u+3)(u-2)=0
u=-3 or 2
..
for u=-3
-3=1/(x-2)
-3x+6=1
3x=5
x=5/3
..
for u=2
2=1/(x-2)
2x-4=1
2x=5
x=5/2
..
2. 2/(x+1) - 5/(sqrt x+1) +3 =0
2/(x+1)-5/√(x+1)+3=0
let u=1/√(x+1)
u^2=1/(x+1)
2u^2-5u+3=0
(u-1)(2u-3)=0
u=1 or 3/2
..
For u=1
1=1/√(x+1)
√(x+1)=1
square both sides
x+1=1
x=0
..
for u=3/2
3/2=1/√(x+1)
3√(x+1)=2
square both sides
9(x+1)=4
9x+9=4
9x=-5
x=-5/9

SOLUTION: solve the following equations. 1. 1/(x-2)^2 + 1/(x-2) -6 =0 2. 2/(x+1) - 5/(sqrt x+1) +3 =0