What is ((2x^3+4x^2+2x))/((6x^3-6x)) ?

The solution to ((2x^3+4x^2+2x))/((6x^3-6x)) is (x+1)/(3(x-1))

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simplify ((2x^3+4x^2+2x))/((6x^3-6x))

simplify

\frac{( 2 x ^{3} + 4 x ^{2} + 2 x )}{( 6 x ^{3} - 6 x )}

\frac{x + 1}{3 ( x - 1 )}

Solution steps

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

Factor

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

= \frac{2 x ( x + 1 ) ^{2}}{6 x ^{3} - 6 x}

Factor

6 x^{3} - 6 x : 6 x (x + 1) (x - 1)

= \frac{2 x ( x + 1 ) ^{2}}{6 x ( x + 1 ) ( x - 1 )}

Cancel the common factor:

x

= \frac{2 ( x + 1 ) ^{2}}{6 ( x + 1 ) ( x - 1 )}

Factor the number:

6 = 2 \cdot 3

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

Cancel the common factor:

2

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x + 1

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

cos^{3} (x) + cos (x)

\frac{n !}{n ! ( n + 1 )}

\frac{- 56 x y ^{5} z ^{2}}{- 8 x y ^{2} z ^{2}}

8 a^{2} b (a - b)^{2} - 4 a^{2} (a - b)^{3}

1.4 \cdot 1 0^{18}

What is ((2x^3+4x^2+2x))/((6x^3-6x)) ?
The solution to ((2x^3+4x^2+2x))/((6x^3-6x)) is (x+1)/(3(x-1))