Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

To write as a fraction with a common denominator, multiply by .

Multiply and .

Reorder the factors of .

Combine the numerators over the common denominator.

Apply the distributive property.

Multiply by .

Move to the left of .

Add and .

Add and .

Rewrite in a factored form.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Cancel the common factor.

Rewrite the expression.

Simplify x/(x-1)+(2x-1)/(x^2-3x+2)