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2 years ago

Simplify....

1 answer:

6 0

The simplified expression of $\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}$ is $\frac{8a}{a^8 - 1}$

<h3>How to simplify the expression?</h3>

The expression is given as:

$\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}$

Add the first two terms

$\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}$

Evaluate

$\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}$

Evaluate the first two terms

$\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}$

Evaluate

$\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}$

Take the LCM

$\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}$

Evaluate the like terms

$\frac{8a}{a^8 - 1}$

Hence, the simplified expression is $\frac{8a}{a^8 - 1}$

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A = 2 4 b = (3 -2 Work out 3a + b as a column vector.

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As a column vector 3a +b = (9,10)

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