What is expand ((t^4+3t^2)^2)/(9(t^2+1)^4) ?

The solution to expand ((t^4+3t^2)^2)/(9(t^2+1)^4) is (t^8+6t^6+9t^4)/(9t^8+36t^6+54t^4+36t^2+9)

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expand ((t^4+3t^2)^2)/(9(t^2+1)^4)

expand

\frac{( t ^{4} + 3 t ^{2} ) ^{2}}{9 ( t ^{2} + 1 ) ^{4}}

\frac{t ^{8} + 6 t ^{6} + 9 t ^{4}}{9 t ^{8} + 36 t ^{6} + 54 t ^{4} + 36 t ^{2} + 9}

Solution steps

\frac{( t ^{4} + 3 t ^{2} ) ^{2}}{9 ( t ^{2} + 1 ) ^{4}}

(t^{2} + 1)^{4} = t^{8} + 4 t^{6} + 6 t^{4} + 4 t^{2} + 1

= \frac{( t ^{4} + 3 t ^{2} ) ^{2}}{9 ( t ^{8} + 4 t ^{6} + 6 t ^{4} + 4 t ^{2} + 1 )}

(t^{4} + 3 t^{2})^{2} = t^{8} + 6 t^{6} + 9 t^{4}

= \frac{t ^{8} + 6 t ^{6} + 9 t ^{4}}{9 ( t ^{8} + 4 t ^{6} + 6 t ^{4} + 4 t ^{2} + 1 )}

Expand

9 (t^{8} + 4 t^{6} + 6 t^{4} + 4 t^{2} + 1) : 9 t^{8} + 36 t^{6} + 54 t^{4} + 36 t^{2} + 9

= \frac{t ^{8} + 6 t ^{6} + 9 t ^{4}}{9 t ^{8} + 36 t ^{6} + 54 t ^{4} + 36 t ^{2} + 9}

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

(u cos (v) + u sin (v)) (u cos (v) - u sin (v))

F (- 2, - 8) d i rec t r i z - 10

5 (53 - 9)

(2 x^{3} - ((\frac{2}{3}) x^{3})) - (- 2 x^{3} + ((\frac{2}{3}) x^{3}) = 440)

What is expand ((t^4+3t^2)^2)/(9(t^2+1)^4) ?
The solution to expand ((t^4+3t^2)^2)/(9(t^2+1)^4) is (t^8+6t^6+9t^4)/(9t^8+36t^6+54t^4+36t^2+9)