What is (a^4+a^2-2)/(a^6+8) ?

The solution to (a^4+a^2-2)/(a^6+8) is ((a+1)(a-1))/(a^4-2a^2+4)

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simplify (a^4+a^2-2)/(a^6+8)

simplify

\frac{a ^{4} + a ^{2} - 2}{a ^{6} + 8}

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

Solution steps

\frac{a ^{4} + a ^{2} - 2}{a ^{6} + 8}

Factor

a^{4} + a^{2} - 2 : (a + 1) (a - 1) (a^{2} + 2)

= \frac{( a + 1 ) ( a - 1 ) ( a ^{2} + 2 )}{a ^{6} + 8}

Factor

a^{6} + 8 : (a^{2} + 2) (a^{4} - 2 a^{2} + 4)

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

Cancel the common factor:

a^{2} + 2

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

x^{6} + 6 x^{4} + 9 x^{2} + 4

r^{3} - 3 r^{2} + 3 r - 1

35 \cdot 55

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

What is (a^4+a^2-2)/(a^6+8) ?
The solution to (a^4+a^2-2)/(a^6+8) is ((a+1)(a-1))/(a^4-2a^2+4)