How do you express 5x4x24x in partial fractions?

1 Answer
Oct 22, 2016

5x4x24x=4x4+1x

Explanation:

The denominator can be written as x(x4).

We can rewrite this as follows:

Ax4+Bx=5x4x24x

Put on a common denominator.

A(x)+B(x4)=5x4

Ax+Bx4B=5x4

(A+B)x4B=5x4

We can hence write the following system of equations.

A+B=5
4B=4

Solving, we have that B=1 and that A=4

We can now reinsert into the original equation to get our partial fraction decomposition.

4x4+1x=5x4x24x

Let's quickly check the validity of our answer.

What is the sum of 4x4+1x?

Put on a common denominator.

4(x)(x4)(x)+1(x4)x(x4)=4x+x4x(x4)=5x4x24x

This verifies the initial expression, so we have done our decomposition properly.

Hopefully this helps!