Solve the given nonlinear inequality. Write the solution set using interval notation. Graph the solution set.$\frac{x^2-2x+3}{x+1}\le 1$

Key Concepts: Nonlinear Inequalities, Interval Notation, Graphing Explanation: To solve this nonlinear inequality, we will first solve the equality which is obtained by replacing the inequality sign with an equal sign, and then we will identify the intervals that satisfy the inequality. Step by Step Solution: Step 1. Solve the equation: $\frac{x^2-2x+3}{x+1}=1$ Step 2. Simplify the left-hand side: $x-2=0$. Therefore $x=2$ Step 3. Identify the intervals where the inequality holds true. First, note that the inequality is undefined at $x=-1$, so we must exclude this value from our solution. We now need to check whether the inequality is true for values of $x$ less than -1, between -1 and 2, and greater than 2. By testing a value from each interval, we find that the inequality is false for $x<-1$, true for $-1<x<2$, and false for $x>2$. Step 4. Write the solution set in interval notation. The solution set is therefore $(-1,2]$, which includes $x=2$ but excludes $x=-1$. Final Answer: (-1,2]