*English is not my native language. Sorry if i misspelled wrong.
Solve the inequality: (x+1)/sqrt(1-x)< 1
I know that the answer is: (-∞,0) , but i can´t get to it
First: 1-x ≥ 0
x ≤ 1 (-∞,1]
Then I resolve the exercise:
-multiply both sides by sqrt(1-x) and simplify x+1< sqrt(1-x)
-square both sides and cancel out square root (x+1)^2 < 1-x
-expand binomial x^2+2x+1<1-x
-subtract 1-x from both sides and simplify x^2+3x<0
-factor and find signs -3<x<0
-Combine ranges x≤1 and -3<x<0
Answer: (-3,0)
What did I do wrong?
Solve the inequality: (x+1)/sqrt(1-x)< 1
I know that the answer is: (-∞,0) , but i can´t get to it
First: 1-x ≥ 0
x ≤ 1 (-∞,1]
Then I resolve the exercise:
-multiply both sides by sqrt(1-x) and simplify x+1< sqrt(1-x)
-square both sides and cancel out square root (x+1)^2 < 1-x
-expand binomial x^2+2x+1<1-x
-subtract 1-x from both sides and simplify x^2+3x<0
-factor and find signs -3<x<0
-Combine ranges x≤1 and -3<x<0
Answer: (-3,0)
What did I do wrong?