Simplify: 2/(√x +√y) + 3/(√x -√y) - (5√x -√y)/(x-y)


Simplify: $\dfrac{2}{\sqrt{x} +\sqrt{y}} + \dfrac{3}{\sqrt{x} -\sqrt{y}} -\dfrac{5\sqrt{x} -\sqrt{y}}{x -y}$

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,

= $\dfrac{2}{\sqrt{x}+\sqrt{y}}+\dfrac{3}{\sqrt{x}-\sqrt{y}}-\dfrac{5\sqrt{x}-\sqrt{y}}{x-y}$

= $\dfrac{2(\sqrt{x}-\sqrt{y})}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})} +\dfrac{3(\sqrt{x}+\sqrt{y})}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}-\dfrac{5(\sqrt{x}-\sqrt{y}}{x -y}$

= $\dfrac{2\sqrt{x} -2\sqrt{y} +3\sqrt{x}+3\sqrt{y} -5\sqrt{x}- \sqrt{y}}{x-y}$

= $\dfrac{2\sqrt{y}}{x-y}$

= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: We need to match the denominator of every terms. So, multiply First two terms using (a+b)(a-b) = (a² -b²).

Step 3: We have reduced one step of simplification by directly adding the terms without writing the result of step 2. However, remember that we first found the result of step 2 and then added or subtracted all the three terms altogether.

Step 4: On adding and subtracting, we get our desired result. 


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

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Question: : Simplify: 2/(√x +√y) + 3/(√x -√y) - (5√x -√y)/(x-y) | SciPiPupil

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