Simplify: $\frac{2}{a+b}- \frac{2}{a-b}+\frac{4a}{a²-b²}$

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,

= $\frac{2}{a+b}- \frac{2}{a-b}+\frac{4a}{a²-b²}$

= $\frac{2(a-b)}{(a+b)(a-b)}- \frac{2(a+b)}{(a-b)(a+b)}+\frac{4a}{a²-b²}$

= $\frac{2a-2b}{a²-b²}-\frac{2a+2b}{a²-b²}+\frac{4a}{a²-b²}$

= $\frac{2a-2b-(2a+2b)+4a}{a²-b²}$

= $\frac{6a-2b-2a-2b}{a²-b²}$

= $\frac{4a-4b}{a²-b²}$

= $\frac{4(a-b)}{(a+b)(a-b)}$

= $\frac{4}{a+b}$

= 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: We write the answer of the step 2 after multiplying the factors and terms.

Step 4: As all denominators are the same, we add and subtract the terms in the numerator.

Step 5: We perform simple mathematical operations.

Step 6: Here as well, we perform the addition and subtraction.

Step 7: The two terms in the numerator have 4 in common. So, we take the common factor our and re-write the expression. In the denominator, we write the (a²-b²) in its factor form.

Step 8: We write our answer as the term (a-b) which was common in the numerator and denominator gets cancelled and result 1. 


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Question: Simplify: 2/(a+b) -2/(a-b) +4a/(a²-b²) . | Simplification of Rational Expressions | SciPiPupil

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