Answer:
[tex]\large\boxed{(f+g)(x)=2x^2+\dfrac{3}{2}x-5}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-2=\dfrac{1}{2}x-2\\\\g(x)=2x^2+x-3\\\\(f+g)(x)=\left(\dfrac{1}{2}x-2\right)+(2x^2+x-3)\\\\=\dfrac{1}{2}x-2+2x^2+x-3\qquad\text{combine like terms}\\\\=2x^2+\left(\dfrac{1}{2}x+x\right)+(-2-3)\\\\=2x^2+1\dfrac{1}{2}x-5\\\\=2x^2+\dfrac{3}{2}x-5[/tex]
