What is (x-5)/(10x-2)*(25x^2-1)/(x^2-10x+25) ?

The solution to (x-5)/(10x-2)*(25x^2-1)/(x^2-10x+25) is (5x+1)/(2(x-5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x-5)/(10x-2)*(25x^2-1)/(x^2-10x+25)

simplify

\frac{x - 5}{10 x - 2} \cdot \frac{25 x ^{2} - 1}{x ^{2} - 10 x + 25}

\frac{5 x + 1}{2 ( x - 5 )}

Solution steps

\frac{x - 5}{10 x - 2} \cdot \frac{25 x ^{2} - 1}{x ^{2} - 10 x + 25}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( x - 5 ) ( 25 x ^{2} - 1 )}{( 10 x - 2 ) ( x ^{2} - 10 x + 25 )}

Factor

x^{2} - 10 x + 25 : (x - 5)^{2}

= \frac{( x - 5 ) ( 25 x ^{2} - 1 )}{( 10 x - 2 ) ( x - 5 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= \frac{( x - 5 ) ( 25 x ^{2} - 1 )}{( 10 x - 2 ) ( x - 5 ) ( x - 5 )}

Cancel the common factor:

x - 5

= \frac{25 x ^{2} - 1}{( 10 x - 2 ) ( x - 5 )}

Factor

25 x^{2} - 1 : (5 x + 1) (5 x - 1)

= \frac{( 5 x + 1 ) ( 5 x - 1 )}{( 10 x - 2 ) ( x - 5 )}

Factor

10 x - 2 : 2 (5 x - 1)

= \frac{( 5 x + 1 ) ( 5 x - 1 )}{2 ( 5 x - 1 ) ( x - 5 )}

Cancel the common factor:

5 x - 1

= \frac{5 x + 1}{2 ( x - 5 )}

\frac{x ^{2} - 36}{x ^{2} - 5 x - 6} \cdot \frac{3 x + 3}{9 x ^{2}}

\frac{2 + x - \frac{x ^{2}}{4} + \frac{x ^{3}}{24}}{x}

- 3 - \frac{1}{4}

5 x (3 x + 2) - 4 (3 x + 2)

What is (x-5)/(10x-2)*(25x^2-1)/(x^2-10x+25) ?
The solution to (x-5)/(10x-2)*(25x^2-1)/(x^2-10x+25) is (5x+1)/(2(x-5))