Question

Solve the inequality by using the graph of the function.

Solve $R\left(x\right)<0$, where$R\left(x\right)=\frac{x}{(x-1)(x+2)}$

Short answer

The solution of the inequality is $(-\infty ,-2)\cup (0,1)$.

Step-by-step solution

Step 1. Given Information 

We are given a function,

$R\left(x\right)=\frac{x}{(x-1)(x+2)}$

Step 2. Graphing the function  

The graph of the function is as follows,

Step 3. Solution of the inequality  

As seen from the graph, $R\left(x\right)<0$for $(-\infty ,-2)\cup (0,1)$.

Hence the solution is $(-\infty ,-2)\cup (0,1)$.