Simplify: $\frac{a+2}{1+a+a²}- \frac{a-2}{1-a+a²}-\frac{2a²}{1+a²+a⁴}$

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,

= $\frac{a+2}{1+a+a²}- \frac{a-2}{1-a+a²}-\frac{2a²}{1+a²+a⁴}$

= $\frac{(a+2)(1-a+a²)}{(1+a+a²)(1-a+a²)}- \frac{(a-2)(1+a+a²)}{(1-a+a²)(1+a+a²)}$
$-\frac{2a²}{1+a²+a⁴}$

= $\frac{(a+2)(1-a+a²) - (a-2)(1+a+a²)}{(1+a+a²)(1-a+a²)}-\frac{2a²}{1+a²+a⁴}$

= $\frac{a-a²+a³+2-2a+2a²-(a+a²+a³-2-2a-2a²)}{(1+a²)²-a²}$
$-\frac{2a²}{1+a²+a⁴}$

= $\frac{a³+a²-a+2-a³+a+a²+2}{1+2a²+a⁴-a²} -\frac{2a²}{1+a²+a⁴}$

= $\frac{2a²+4-2a²}{1+a²+a⁴}$

= $\frac{4}{1+a²+a⁴}$


= Answer


Explanation to the above answer.


Step 1: Copy the same question given.

Step 2: If we want to take the LCM between 3 and 4. We multiply both. We do the same here for the first two terms.

Step 3: Since we have common denominators, we subtract the two terms. 

Step 4: Now, we multiply the factors and write their result in expressions. Also in the denominator we have expression in the form of (a+b)(a-b) which we can write as a²-b².

Step 5: Open the minus sign and perform the required operations in the numerator as well as denominator.

Step 6: Combine the two terms because the Denominators are equal. 

Step 7: Write your answer by performing required operations.



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Question: Simplify: (x+3)/(x²+3x+9) + (x-3)/(x²-3x+9) - 54/(x⁴+9x²+81) | Simplification of Rational Expressions | SciPiPupil

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