What is [ 1/((x-1)^{-1)}-(1/1)/((x-2)^{-2)}]^2 ?

The solution to [ 1/((x-1)^{-1)}-(1/1)/((x-2)^{-2)}]^2 is (-x^2+5x-5)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify [ 1/((x-1)^{-1)}-(1/1)/((x-2)^{-2)}]^2

simplify

[\frac{1}{( x - 1 ) ^{- 1}} - \frac{\frac{1}{1}}{( x - 2 ) ^{- 2}}]^{2}

(- x^{2} + 5 x - 5)^{2}

Solution steps

(\frac{1}{( x - 1 ) ^{- 1}} - \frac{\frac{1}{1}}{( x - 2 ) ^{- 2}})^{2}

\frac{1}{( x - 1 ) ^{- 1}} = x - 1

\frac{\frac{1}{1}}{( x - 2 ) ^{- 2}} = (x - 2)^{2}

= (x - 1 - (x - 2)^{2})^{2}

Expand

- (x - 2)^{2} : - x^{2} + 4 x - 4

= (x - 1 - x^{2} + 4 x - 4)^{2}

Group like terms

= (- x^{2} + x + 4 x - 1 - 4)^{2}

Add similar elements:

x + 4 x = 5 x

= (- x^{2} + 5 x - 1 - 4)^{2}

Subtract the numbers:

- 1 - 4 = - 5

= (- x^{2} + 5 x - 5)^{2}

(e^{x})^{2} - 4 x y

\frac{\frac{b}{a}}{( - 3 )}

\frac{5 - 5}{x ^{2} + 1}

0.8 q - 0.7 (5 q - 4)

- 2 (3 x - 4)

What is [ 1/((x-1)^{-1)}-(1/1)/((x-2)^{-2)}]^2 ?
The solution to [ 1/((x-1)^{-1)}-(1/1)/((x-2)^{-2)}]^2 is (-x^2+5x-5)^2