Answer
$\frac{1}{x}-\frac{2}{x^2}-\frac{4}{x^3}+\frac{3}{x^4}$
Work Step by Step
Step 1. Assume the end results as: $\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x^4}$
Step 2. Combine the above functions as:
$\frac{Ax^3+Bx^2+Cx+D}{x^4}$
Step 3. Compare the above result with the original expression to get $A=1, B=-2, C=-4, D=3$
Step 4. Write the final results as:
$\frac{1}{x}-\frac{2}{x^2}-\frac{4}{x^3}+\frac{3}{x^4}$
