What is expand (t^4-1)/(t^3-1) ?

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

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expand (t^4-1)/(t^3-1)

expand

\frac{t ^{4} - 1}{t ^{3} - 1}

\frac{t ^{3} + t ^{2} + t + 1}{t ^{2} + t + 1}

Solution steps

\frac{t ^{4} - 1}{t ^{3} - 1}

Factor

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

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

Factor

t^{3} - 1 : (t - 1) (t^{2} + t + 1)

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

Cancel the common factor:

t - 1

= \frac{( t ^{2} + 1 ) ( t + 1 )}{t ^{2} + t + 1}

Expand

(t^{2} + 1) (t + 1) : t^{3} + t^{2} + t + 1

= \frac{t ^{3} + t ^{2} + t + 1}{t ^{2} + t + 1}

3 (4 e^{2 x} + e^{3 x})

\frac{1}{s ^{2} ( s ^{2} + 2 s + 1 )}

3 a (a^{2} - 2 a = 4)

\frac{n ( n - 2 ) ( 2 n + 7 )}{6}

\frac{3 ( 5 - 3 y )}{2}

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