What is (27x^6+1)/(3x^2+1) ?

The solution to (27x^6+1)/(3x^2+1) is (3x^2+1+3x)(3x^2+1-3x)

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simplify (27x^6+1)/(3x^2+1)

simplify

\frac{27 x ^{6} + 1}{3 x ^{2} + 1}

(3 x^{2} + 1 + 3 x) (3 x^{2} + 1 - 3 x)

Solution steps

\frac{27 x ^{6} + 1}{3 x ^{2} + 1}

Apply exponent rules

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

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

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

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

Factor

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

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

Cancel the common factor:

3 x^{2} + 1

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

(a + 3) (a^{2} + 9) (a - 3)

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

\frac{1}{a x} - \frac{1}{a ^{2} + a x} + \frac{1}{a + x}

\frac{x ^{2} + 2 x}{x ^{2} + 4 x + 4}

\frac{3}{2} \div \frac{8}{3}

What is (27x^6+1)/(3x^2+1) ?
The solution to (27x^6+1)/(3x^2+1) is (3x^2+1+3x)(3x^2+1-3x)