Question

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

Short answer

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

Step-by-step solution

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 3x2-5x+1x

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

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