Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

If $x=-2$, the value of the expression $3x^2-5x+\frac{1}{x}$ is _______.

Step-by-Step Solution

Answer

The value of expression is $\frac{43}{2}$.

Step 1. Given Information

If $x=-2$, the value of the expression $3x^2-5x+\frac{1}{x}$ is _______.

Step 2. The given expression is 3 x 2 - 5 x + 1 x

We find the value of expression after putting $x=-2$.

Step 3. Putting x = - 2 in the given expression

$=3{(-2)}^2-5(-2)+\frac{1}{(-2)}$

Simplifying the expression

$$\begin{gathered} =3\times 4+10-\frac{1}{2} \\ =12+10-\frac{1}{2} \\ =22-\frac{1}{2} \end{gathered}$$

Step 4. The LCD is 2.

So$=22\times \frac{2}{2}-\frac{1}{2}$

$$\begin{gathered} =\frac{44}{2}-\frac{1}{2} \\ =\frac{44-1}{2} \\ =\frac{43}{2} \end{gathered}$$