Answer
$-\frac{x^{2}}{8}+x-1$
Work Step by Step
We are given the expression $(\frac{3x^{2}}{16}+\frac{5x}{8}-\frac{1}{4})-(\frac{5x^{2}}{16}-\frac{3x}{8}+\frac{3}{4})$. We can subtract the second polynomial from the first polynomial by adding the opposite of the second polynomial to the first polynomial.
$(\frac{3x^{2}}{16}+\frac{5x}{8}-\frac{1}{4})+(-\frac{5x^{2}}{16}+\frac{3x}{8}-\frac{3}{4})$
We can combine like terms to simplify.
$(\frac{3x^{2}}{16}-\frac{5x^{2}}{16})+(\frac{5x}{8}+\frac{3x}{8})+(-\frac{1}{4}-\frac{3}{4})=-\frac{2x^{2}}{16}+\frac{8x}{8}-\frac{4}{4}=-\frac{x^{2}}{8}+x-1$
