Algebra Simplification

Question

Show step by step why/how the left side equals the right side.

Answer 1

The Expression on the left hand side is

Now let us first consider the expression along the Square root.

Simplify the Expression.

Now Multiply and Divide with √2

Now substitute the above in the expression and simplify.

Therefore the expression is simplified as

.

Comments

Thank you for an excellent step by step explanation. However, your final result has a 2(x+1) in the denominator but the result I posted has just (x+1). Which answer is correct? Also, in the second last step you wrote 2x^2+3x+2 in the radical, is  this a mistake? I would think that it would be 2x^2+2. You return to 2(x^2+1) in the final answer, so why then even expand in the second last step?

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The second last step is a typing mistake. Please do not consider the step.

And the final answer consisting of 2(x+1) in the denominator is the correct solution.