What is (t+2)^2*t(t+1)>t^2*(t+1)^2 ?

The solution to (t+2)^2*t(t+1)>t^2*(t+1)^2 is -4/3 0

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(t+2)^2t(t+1)>t^2(t+1)^2

(t + 2)^{2} \cdot t (t + 1) > t^{2} \cdot (t + 1)^{2}

- \frac{4}{3} < t < - 1 or t > 0

Interval Notation

(- \frac{4}{3}, - 1) \cup (0, \infty)

Decimal Notation

- 1.33333 \dots < t < - 1 or t > 0

Solution steps

(t + 2)^{2} t (t + 1) > t^{2} (t + 1)^{2}

Rewrite in standard form

3 t^{3} + 7 t^{2} + 4 t > 0

Factor

3 t^{3} + 7 t^{2} + 4 t : t (t + 1) (3 t + 4)

t (t + 1) (3 t + 4) > 0

Identify the intervals

- \frac{4}{3} < t < - 1 or t > 0

\frac{lo g _{10} ( 1 )}{2 ( 5 - 2 x )} < 0

x (x^{2} - 4) \leq 0

\frac{( 2 x + 5 )}{( x + 7 )} > 3

(x + 10)^{2} < 1

\frac{( ( x ^{2} - 81 ) ( x - 9 ) )}{( ( x - 1 ) ( x - 6 ) )} \geq 0

What is (t+2)^2*t(t+1)>t^2*(t+1)^2 ?
The solution to (t+2)^2*t(t+1)>t^2*(t+1)^2 is -4/3 <t<-1\lor t>0