Simplify: 1/8(x-1) + 1/8(x+1) + 2√x/8(x-1)


Simplify: $\dfrac{1}{8(\sqrt{x} -\sqrt{1})} + \dfrac{1}{8(\sqrt{x} +\sqrt{1})} +\dfrac{2\sqrt{x}}{8(x -1)}$

This is a class 10 Question From Simplification of Rational Expressions chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the description below. 

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Solution:

Given,

= $\dfrac{1}{8(\sqrt{x} -\sqrt{1})} + \dfrac{1}{8(\sqrt{x} +\sqrt{1})} +\dfrac{2\sqrt{x}}{8(x -1)}$

= $\dfrac{1}{8} \left (\dfrac{1}{(\sqrt{x} -\sqrt{1})} + \dfrac{1}{(\sqrt{x} +\sqrt{1})} +\dfrac{2\sqrt{x}}{(x -1)}\right )$

= $\dfrac{1}{8} \left ( \dfrac{1(\sqrt{x} +\sqrt{1})}{(\sqrt{x} -\sqrt{1})(\sqrt{x} +\sqrt{1}) } + \dfrac{1(\sqrt{x} -\sqrt{1})}{(\sqrt{x} +\sqrt{1})(\sqrt{x} -\sqrt{1}) } +\dfrac{2\sqrt{x}}{(x -1)}\right )$

= $\dfrac{1}{8} \left (  \dfrac{\sqrt{x} +\sqrt{1}+\sqrt{x} -\sqrt{1} +2\sqrt{x}}{x-1} \right )$

= $\dfrac{1}{8} \left ( \dfrac{4\sqrt{x}}{x-1} \right )$

= $\dfrac{\sqrt{x}}{2(x-1)}$

= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: Take 1/8 common from all the terms to make it easy for simplification.

Step 3: Make the denominator equal by using formula of (a+b)(a-b) = (a²-b²). Using this, we get our denominator equal. 

Step 4: As all the denominators are equal, we can now add or subtract the terms. So, we do that.

Step 5: Write the result of addition.

Step 6: 4 in the numerator and 8 in the denominator, as they are in division form with no addition or subtraction sign,we can divide and get 1/2. Using this,we get our answer.


Here is the Website link to the guide of Simplification of Rational Expressions.

Here is the Page link to all the solutions of Simplification of Rational Expressions.


Question: : Simplify: 1/8(x-1) + 1/8(x+1) + 2√x/8(x-1) | SciPiPupil

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