What is ((5x-x^2+(x-5)^2))/((10x-2x^2)) ?

The solution to ((5x-x^2+(x-5)^2))/((10x-2x^2)) is 5/(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((5x-x^2+(x-5)^2))/((10x-2x^2))

simplify

\frac{( 5 x - x ^{2} + ( x - 5 ) ^{2} )}{( 10 x - 2 x ^{2} )}

\frac{5}{2 x}

Solution steps

\frac{5 x - x ^{2} + ( x - 5 ) ^{2}}{10 x - 2 x ^{2}}

Expand

5 x - x^{2} + (x - 5)^{2} : - 5 x + 25

= \frac{- 5 x + 25}{10 x - 2 x ^{2}}

Factor

- 5 x + 25 : 5 (- x + 5)

= \frac{5 ( - x + 5 )}{10 x - 2 x ^{2}}

Factor

10 x - 2 x^{2} : 2 x (5 - x)

= \frac{5 ( - x + 5 )}{2 x ( 5 - x )}

Apply the commutative law:

5 - x = - x + 5

= \frac{5 ( - x + 5 )}{2 x ( - x + 5 )}

Cancel the common factor:

- x + 5

= \frac{5}{2 x}

\frac{a}{b} + \frac{b}{a} + 2

\frac{1 0 ^{5} + 1 0 ^{4} + 1 0 ^{3} - 5 x 1 0 ^{4}}{104}

(4 x - 8)^{3}

y + 5 (x^{8}) - 21

(\frac{7 x}{3 y})^{2}

What is ((5x-x^2+(x-5)^2))/((10x-2x^2)) ?
The solution to ((5x-x^2+(x-5)^2))/((10x-2x^2)) is 5/(2x)