What is expand ((x^4+3x+1)^5)/((x^4-3x^2+1)^4) ?

The solution to expand ((x^4+3x+1)^5)/((x^4-3x^2+1)^4) is

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expand ((x^4+3x+1)^5)/((x^4-3x^2+1)^4)

expand

\frac{( x ^{4} + 3 x + 1 ) ^{5}}{( x ^{4} - 3 x ^{2} + 1 ) ^{4}}

\frac{x ^{20} + 15 x ^{17} + 5 x ^{16} + 90 x ^{14} + 60 x ^{13} + 10 x ^{12} + 270 x ^{11} + 270 x ^{10} + 90 x ^{9} + 415 x ^{8} + 540 x ^{7} + 270 x ^{6} + 303 x ^{5} + 410 x ^{4} + 270 x ^{3} + 90 x ^{2} + 15 x + 1}{x ^{16} - 12 x ^{14} + 58 x ^{12} - 144 x ^{10} + 195 x ^{8} - 144 x ^{6} + 58 x ^{4} - 12 x ^{2} + 1}

Solution steps

\frac{( x ^{4} + 3 x + 1 ) ^{5}}{( x ^{4} - 3 x ^{2} + 1 ) ^{4}}

(x^{4} - 3 x^{2} + 1)^{4} = x^{16} - 12 x^{14} + 58 x^{12} - 144 x^{10} + 195 x^{8} - 144 x^{6} + 58 x^{4} - 12 x^{2} + 1

= \frac{( x ^{4} + 3 x + 1 ) ^{5}}{x ^{16} - 12 x ^{14} + 58 x ^{12} - 144 x ^{10} + 195 x ^{8} - 144 x ^{6} + 58 x ^{4} - 12 x ^{2} + 1}

(x^{4} + 3 x + 1)^{5} = x^{20} + 15 x^{17} + 5 x^{16} + 90 x^{14} + 60 x^{13} + 10 x^{12} + 270 x^{11} + 270 x^{10} + 90 x^{9} + 415 x^{8} + 540 x^{7} + 270 x^{6} + 303 x^{5} + 410 x^{4} + 270 x^{3} + 90 x^{2} + 15 x + 1

= \frac{x ^{20} + 15 x ^{17} + 5 x ^{16} + 90 x ^{14} + 60 x ^{13} + 10 x ^{12} + 270 x ^{11} + 270 x ^{10} + 90 x ^{9} + 415 x ^{8} + 540 x ^{7} + 270 x ^{6} + 303 x ^{5} + 410 x ^{4} + 270 x ^{3} + 90 x ^{2} + 15 x + 1}{x ^{16} - 12 x ^{14} + 58 x ^{12} - 144 x ^{10} + 195 x ^{8} - 144 x ^{6} + 58 x ^{4} - 12 x ^{2} + 1}

(1 + sin (x)) (1 + cos (x))

\frac{( x ^{4} + 1 ) ^{2}}{x ^{8} + 1}

(x^{3} - x + 30)^{6}

(3 + 2)^{5}

122 (e^{(- 0.18 t)} - e^{(- t)})

What is expand ((x^4+3x+1)^5)/((x^4-3x^2+1)^4) ?
The solution to expand ((x^4+3x+1)^5)/((x^4-3x^2+1)^4) is