Simplify: 1/(a-1) -3/a +3/(a+1) -1/(a+2) | SciPiPupil

Simplify: $\dfrac{1}{a-1} - \dfrac{3}{a} +\dfrac{3}{a+1} -\dfrac{1}{a+2}$

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,

=  $\dfrac{1}{a-1} - \dfrac{3}{a} +\dfrac{3}{a+1} -\dfrac{1}{a+2}$

=  $\dfrac{1}{a-1} + \dfrac{3}{a+1} -\left ( \dfrac{3}{a} +\dfrac{1}{a+2} \right )$

= $\dfrac{1(a+1)}{(a-1)(a+1)} +\dfrac{3(a-1)}{(a+1)(a-1)} -\left ( \dfrac{3(a+2) +1(a)}{a(a+2)} \right )$

= $\dfrac{a+1}{a²-1} +\dfrac{3a -3}{a²-1} -\left ( \dfrac{3a +6+a}{a(a+2)} \right)$

= $\dfrac{a+1+3a-3}{a²-1} -\dfrac{4a+6}{a(a+2)}$

= $\dfrac{a(4a-2)(a+2) -\{(4a+6)(a²-1)\}}{a(a+2)(a²-1)}$

= $\dfrac{a(4a²+8a-2a-4) -\{4a³-4a+6a²-6\}}{a(a+2)(a²-1)}$

= $\dfrac{4a³+6a²-4a-4a³+4a-6a²+6}{a(a+2)(a²-1)}$

= $\dfrac{6}{a(a+2)(a²-1)}$

= Answer

Explanation to the above answer.

Step 1: Copy the same question given.

Step 2: Change the order of the terms to make it easy to simplify. 

Step 3: Take LCM of the terms.  

Step 4: Write the answer of step 3.

Step 5: Add or subtract the terms. 

Step 6: Take LCM of the remaining two terms.

Step 7-9: Perform simple mathematics.

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/(a-1) -3/a +3/(a+1) -1/(a+2) | SciPiPupil

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