What is (3k)/(k+1)*(k^2-1)/(3k^3) ?

The solution to (3k)/(k+1)*(k^2-1)/(3k^3) is (k-1)/(k^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (3k)/(k+1)*(k^2-1)/(3k^3)

simplify

\frac{3 k}{k + 1} \cdot \frac{k ^{2} - 1}{3 k ^{3}}

\frac{k - 1}{k ^{2}}

Solution steps

\frac{3 k}{k + 1} \cdot \frac{k ^{2} - 1}{3 k ^{3}}

Apply the fraction rule:

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

= \frac{3 k ( k ^{2} - 1 )}{( k + 1 ) \cdot 3 k ^{3}}

Cancel the common factor:

3

= \frac{k ( k ^{2} - 1 )}{( k + 1 ) k ^{3}}

Apply exponent rule:

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

k^{3} = k k^{2}

= \frac{k ( k ^{2} - 1 )}{( k + 1 ) k k ^{2}}

Cancel the common factor:

k

= \frac{k ^{2} - 1}{( k + 1 ) k ^{2}}

Factor

k^{2} - 1 : (k + 1) (k - 1)

= \frac{( k + 1 ) ( k - 1 )}{( k + 1 ) k ^{2}}

Cancel the common factor:

k + 1

= \frac{k - 1}{k ^{2}}

6 > x

(x + 3)^{2} (x - 7) < 0

20 x^{2} - 45 = 0

5 x^{2} + 6 x + 5 = 2 (2 x^{2} + 10) - 4 x

0 = 19.23 x + 3.25 x^{2}

What is (3k)/(k+1)*(k^2-1)/(3k^3) ?
The solution to (3k)/(k+1)*(k^2-1)/(3k^3) is (k-1)/(k^2)