What is (x^{10}-1)/(3x^9+3x^4) ?

The solution to (x^{10}-1)/(3x^9+3x^4) is ((x-1)(x^4+x^3+x^2+x+1))/(3x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x^{10}-1)/(3x^9+3x^4)

simplify

\frac{x ^{10} - 1}{3 x ^{9} + 3 x ^{4}}

\frac{( x - 1 ) ( x ^{4} + x ^{3} + x ^{2} + x + 1 )}{3 x ^{4}}

Solution steps

\frac{x ^{10} - 1}{3 x ^{9} + 3 x ^{4}}

Factor

x^{10} - 1 : (x + 1) (x^{4} - x^{3} + x^{2} - x + 1) (x - 1) (x^{4} + x^{3} + x^{2} + x + 1)

= \frac{( x + 1 ) ( x ^{4} - x ^{3} + x ^{2} - x + 1 ) ( x - 1 ) ( x ^{4} + x ^{3} + x ^{2} + x + 1 )}{3 x ^{9} + 3 x ^{4}}

Factor

3 x^{9} + 3 x^{4} : 3 x^{4} (x + 1) (x^{4} - x^{3} + x^{2} - x + 1)

= \frac{( x + 1 ) ( x ^{4} - x ^{3} + x ^{2} - x + 1 ) ( x - 1 ) ( x ^{4} + x ^{3} + x ^{2} + x + 1 )}{3 x ^{4} ( x + 1 ) ( x ^{4} - x ^{3} + x ^{2} - x + 1 )}

Cancel the common factor:

x + 1

= \frac{( x ^{4} - x ^{3} + x ^{2} - x + 1 ) ( x - 1 ) ( x ^{4} + x ^{3} + x ^{2} + x + 1 )}{3 x ^{4} ( x ^{4} - x ^{3} + x ^{2} - x + 1 )}

Cancel the common factor:

x^{4} - x^{3} + x^{2} - x + 1

= \frac{( x - 1 ) ( x ^{4} + x ^{3} + x ^{2} + x + 1 )}{3 x ^{4}}

\frac{4 ( m ^{4} ) ^{3}}{5 m ^{5}}

\frac{20 x ^{3} - 10 x ^{2} + 6 x}{2 x + 4}

\frac{2}{3} (\frac{3}{2})

\frac{2}{5} \times 6

x y^{3} 9 x^{2} y^{6}

What is (x^{10}-1)/(3x^9+3x^4) ?
The solution to (x^{10}-1)/(3x^9+3x^4) is ((x-1)(x^4+x^3+x^2+x+1))/(3x^4)