Simplify: a³/(a-1) +a³/(a+1) -1/(a-1) +1/(a+1)


Simplify: $\dfrac{a³}{a-1} + \dfrac{a³}{a+1} -\dfrac{1}{a-1} +\dfrac{1}{a+1}$

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. 

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Solution:

Given,

= $\dfrac{a³}{a-1} + \dfrac{a³}{a+1} -\dfrac{1}{a-1} +\dfrac{1}{a+1}$

= $\dfrac{a³}{a-1} - \dfrac{1}{a-1} +\dfrac{a³}{a+1} +\dfrac{1}{a+1}$

= $\dfrac{a³-1}{a-1} +\dfrac{a³+1}{a+1}$

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

= $a²+a+1 + a²-a+1$

= $2a² +2$

= $2(a² +1)$

= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: Arrange the terms on the basis of like denominators.

Step 3: Add or subtract the like terms.  

Step 4: Expand the terms using formula; (a³+b³)=(a+b)(a²-ab+b³) and (a³-b³)=(a-b)(a²+ab+b²).

Step 5: Same terms in the numerator and denominator get cancelled.

Step 6: Write the result of addition. 

Step 7: Take 2 common and write the remaining expression as your answer.


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: a³/(a-1) +a³/(a+1) -1/(a-1) +1/(a+1) | SciPiPupil

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