Show that (2-√x) ^2 divided by √x can be written as 4x^ (-1/2) - 4+x^1/2

Question

Nikita

Mathematics

22 October, 03:57

Show that (2-√x) ^2 divided by √x can be written as 4x^ (-1/2) - 4+x^1/2

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Answers (1)

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Julio Aguirre · Answer 1

Hello:

(2-√x) ^2 = 4 - 4√x + x (identity : (a-b) ² = a² - 2ab + b² and : (√x) ² = x)

now:

(4 - 4√x + x) / (√x) = 4/√x - 4√x / √x + x / √x

but:

4/√x = 4/x^1/2 = 4x^ (-1/2)

- 4√x / √x = - 4

x / √x = (√x * √x) / √x = √x = x^1/2

conclusion:

(4 - 4√x + x) / (√x) = 4x^ (-1/2) - 4 + x^1/2