Simplify: 1/(a-3) - 1/(a-1) +1/(a+3) -1/(a+1)


Simplify: $\dfrac{1}{a-3} -\dfrac{1}{a-1} +\dfrac{1}{a+3} -\dfrac{1}{a+1}$

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

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Solution:

Given,

= $\dfrac{1}{a-3} -\dfrac{1}{a-1} -\dfrac{1}{a+3} -\dfrac{1}{a+1}$

= $\dfrac{1}{a-3} +\dfrac{1}{a+3} -\left (\dfrac{1}{a-1} +\dfrac{1}{a+1} \right )$

= $\dfrac{1(a+3)}{(a-3)(a+3)} +\dfrac{1(a-3)}{(a+3)(a-3)} -\left (\dfrac{1(a+1)}{(a-1)(a+1)} +\dfrac{1(a-1)}{(a+1)(a-1)} \right )$

= $\dfrac{a+3}{a²-9} +\dfrac{a-3}{a²-9} -\left (\dfrac{a+1}{a²-1} +\dfrac{a-1}{a²-1} \right )$

= $\dfrac{a+3+a-3}{a²-9} -\left (\dfrac{a+1+a-1}{a²-1}\right )$

= $\dfrac{2a}{a²-9} -\left (\dfrac{2a}{a²-1}\right )$

= $\dfrac{2a(a²-1)-2a(a²-9)}{(a²-9)(a²-1)}$

= $\dfrac{2a³-2a -2a³+18a}{(a²-1)(a²-9)}$

= $\dfrac{16a}{(a²-1)(a²-9)}$

= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: Keep the similar denominators at one side and the other denominators at other side. 

Step 3: Take the LCM between the first two and the last two terms. 

Step 4: Write the answer that you get after multiplying in step 3. 

Step 5: Now, add the first two terms and the last two terms seperately.

Step 6: Write the answer of step 5.

Step 7: Take LCM of the remaining two terms and perform mathematics accordingly.

Step 8: Write the answer after multiplying in step 7.

Step 9: Write your answer by adding or subtracting the terms in step 8.


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Question: Simplify: 1/(a-3) - 1/(a-1) +1/(a+3) -1/(a+1) | SciPiPupil

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