Question

Solve the given nonlinear inequality. Write the solution set using interval notation.
x2 − 3x + 4/x + 1 ≤ 1

Answer 1

\[x ^{2}3x+4/x+1\le1\]

Answer 2

I guess that the inequality really is:
\[x^2 - 3x + \frac {4}{x}+1\le1\]
This is the same as:
\[x^2-3x+\frac{4}{x}\le0\]
I rewrite the equation
\[x^2-3x+\frac{4}{x}=0\]
by guessing the solution x=-1 and get the following:
\[(x+1)(x^2-4)=0\]
The ineq can be written as:
\[(x+1)(x-2)(x+2)\le0\]
So it is 0 at x=-2, x=-1 and x=+2
In the inequality will be less than zero when
\[x \le-2\]
or
\[-1 \le x \le 2\]
\[x \in [-\infty,-2]\cup[-1,2] \]