Simplify the expression by factoring, showing the steps in your work.

Given:

To find:

The simplified expression by factoring.

Solution:

Let us factor the numerator:

31x can be written as 3x + 28x.

Take 3x common in 1st two terms and 7 common in next two terms.

Make sure the remaining terms in the both brackets must be same.

Now, take out common factor (4x + 1).

In the same way, factorize the denominator:

8x can be written as 4x + 4x.

Take 4x common in 1st two terms and 1 common in next two terms.

Make sure the remaining terms in the both brackets must be same.

Now, take out common factor (4x + 1).

Substitute the terms we found for numerator and denominator:

Cancel the common factors.

The simplified expression is .