Answer
$-\dfrac{2}{5}x^4+x^3-\dfrac{1}{8}x^2$
Work Step by Step
Consider the given polynomial
$(\dfrac{1}{5}x^4+\dfrac{1}{3}x^3+\dfrac{3}{8}x^2+6)+(-\dfrac{3}{5}x^4+\dfrac{2}{3}x^3-\dfrac{1}{2}x^2-7)$
Need to drop the parentheses.
Thus,
$(\dfrac{1}{5}x^4+\dfrac{1}{3}x^3+\dfrac{3}{8}x^2+6)+(-\dfrac{3}{5}x^4+\dfrac{2}{3}x^3-\dfrac{1}{2}x^2-7)=\dfrac{1}{5}x^4+\dfrac{1}{3}x^3+\dfrac{3}{8}x^2+6-\dfrac{3}{5}x^4+\dfrac{2}{3}x^3-\dfrac{1}{2}x^2-7$
$=\dfrac{1}{5}x^4-\dfrac{3}{5}x^4+\dfrac{1}{3}x^3+\dfrac{2}{3}x^3+\dfrac{3}{8}x^2-\dfrac{1}{2}x^2$
$=-\dfrac{2}{5}x^4+x^3-\dfrac{1}{8}x^2$