# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to1}\left(\frac{\left(\sqrt{x}\right)^2}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right)$

Learn how to solve limits by direct substitution problems step by step online.

$\lim_{x\to1}\left(\frac{x}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right)$

Learn how to solve limits by direct substitution problems step by step online. Evaluate the limit of x^0.5^2 as x approaches 1. Cancel exponents \frac{1}{2} and 2. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2, where:<ul><li>The first term (a) is x.</li><li>The second term (b) is 1.</li></ul>Then:. Evaluate the limit by replacing all occurrences of x by 1. Simplifying.

$1$
$\lim_{x\to1}\left(\frac{\left(\sqrt{x}\right)^2}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right)$