Is This the Correct Way to Simplify Complex Fractions?

[science_rules]

Homework Statement

Simplify: (a² + 2ab + b²)/(a² - b²) times (a² - 2ab + b²)/(a² - b²)

Homework Equations

(a² + 2ab + b²)/(a² - b²) times (a² - 2ab + b²)/(a² - b²)

The Attempt at a Solution

Did I simplify this correctly?? (a+b)(a+b)/((a-b)(a+b)) times (a-b)(a-b)/((a-b)(a+b)) = ((a+b)/(a+b)) times ((a-b)/(a-b))
= (a+b)(a-b)/((a+b)(a-b)) = 1 times 1 = 1 Answer

 

[SammyS]

Homework Statement

Simplify: (a² + 2ab + b²)/(a² - b²) times (a² - 2ab + b²)/(a² - b²)

Homework Equations

(a² + 2ab + b²)/(a² - b²) times (a² - 2ab + b²)/(a² - b²)

The Attempt at a Solution

Did I simplify this correctly?? (a+b)(a+b)/((a-b)(a+b)) times (a-b)(a-b)/((a-b)(a+b)) = ((a+b)/(a+b)) times ((a-b)/(a-b)) = (a+b)(a-b)/((a+b)(a-b)) = 1 times 1 = 1 Answer

That's the correct final result. It's hard to say if your steps are correct. You skipped some steps and regrouped things in some rather curious ways.