The required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).
What is an expression?
An expression is any statement in mathematics written using numbers, variables and at least one operation present.
Simplification of the expression: 2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16
Given an expression,
2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16
On simplifying, we get,
(2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)
For the numerator, (2x - 8).(x² + 5x + 4), we have,
= 2(x + 1)(x - 4)(x + 4)
For the denominator, (x² - 16).(x² + 8x + 16)
= (x + 4)(x - 4)(x + 4)(x + 4)
Now, (2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)
= 2(x + 1)(x - 4)(x + 4) / (x + 4)(x - 4)(x + 4)(x + 4)
= 2(x + 1) / (x + 4)(x + 4)
The restriction to the given expression is that the denominator, x + 4 should not be 0.
Hence, the required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).
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