What is expand (5t(3t^2+25))/(8(t^2+5)^2) ?

The solution to expand (5t(3t^2+25))/(8(t^2+5)^2) is (15t^3+125t)/(8t^4+80t^2+200)

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expand (5t(3t^2+25))/(8(t^2+5)^2)

expand

\frac{5 t ( 3 t ^{2} + 25 )}{8 ( t ^{2} + 5 ) ^{2}}

\frac{15 t ^{3} + 125 t}{8 t ^{4} + 80 t ^{2} + 200}

Solution steps

\frac{5 t ( 3 t ^{2} + 25 )}{8 ( t ^{2} + 5 ) ^{2}}

(t^{2} + 5)^{2} = t^{4} + 10 t^{2} + 25

= \frac{5 t ( 3 t ^{2} + 25 )}{8 ( t ^{4} + 10 t ^{2} + 25 )}

Expand

8 (t^{4} + 10 t^{2} + 25) : 8 t^{4} + 80 t^{2} + 200

= \frac{5 t ( 3 t ^{2} + 25 )}{8 t ^{4} + 80 t ^{2} + 200}

Expand

5 t (3 t^{2} + 25) : 15 t^{3} + 125 t

= \frac{15 t ^{3} + 125 t}{8 t ^{4} + 80 t ^{2} + 200}

\frac{2}{( 2 x - k ) ^{2}}

\frac{( x d x )}{( x + 1 ) ^{8}}

\frac{d}{d t} ((x) (e^{t} (sin (t) + cos (t))))

[(x - 4) (2 x + 1)] x

\frac{s ^{3} + 17}{s ( s ^{2} + 10 s + 34 )}

What is expand (5t(3t^2+25))/(8(t^2+5)^2) ?
The solution to expand (5t(3t^2+25))/(8(t^2+5)^2) is (15t^3+125t)/(8t^4+80t^2+200)