Simplify: $\frac{a+b}{a-b}- \frac{a-b}{a+b}-\frac{2ab}{a²-b²}$

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. If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. 

Solution:

Given,

= $\frac{a+b}{a-b}- \frac{a-b}{a+b}-\frac{2ab}{a²-b²}$

= $\frac{(a+b)(a+b)}{(a-b)(a+b)}- \frac{(a-b)(a-b)}{(a+b)(a-b)}-\frac{2ab}{a²-b²}$

= $\frac{(a+b)^2-(a-b)^2-2ab}{a²-b²}$

= $\frac{a^2+2ab-2ab+b^2-(a^2-2ab+b^2)}{a²-b²}$

= $\frac{a^2+b^2-a^2+2ab-b^2}{a²-b²}$

= $\frac{2ab}{a^2-b^2}$

= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: If we want to take the LCM, we look for the common multiple terms or factors in the denominator. So, we analyse what would be the common denominator? It would probably be (a²-b²) and we know, (a²-b²)=(a+b)(a-b). So, we multiply the first two terms accordingly.

Step 3: As all denominators are the same, we add and subtract the terms in the numerator.

Step 4: We perform simple mathematical operations. Using {(a+b)² = a²+2ab+b²} and {(a-b)²= a²-2ab+b²}

Step 5: Here as well, we perform the addition and subtraction.

Step 6: With simple addition, we get our answer. 2ab/(a²-b²).


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Question: Simplify: (a+b)/(a-b) -(a-b)/(a+b) -(2ab)/(a²-b²). | Simplification of Rational Expressions | SciPiPupil

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