What is expand (2(x+5)^2)/((x^2+2)^2) ?

The solution to expand (2(x+5)^2)/((x^2+2)^2) is (2x^2+20x+50)/(x^4+4x^2+4)

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expand (2(x+5)^2)/((x^2+2)^2)

expand

\frac{2 ( x + 5 ) ^{2}}{( x ^{2} + 2 ) ^{2}}

\frac{2 x ^{2} + 20 x + 50}{x ^{4} + 4 x ^{2} + 4}

Solution steps

\frac{2 ( x + 5 ) ^{2}}{( x ^{2} + 2 ) ^{2}}

(x^{2} + 2)^{2} = x^{4} + 4 x^{2} + 4

= \frac{2 ( x + 5 ) ^{2}}{x ^{4} + 4 x ^{2} + 4}

(x + 5)^{2} = x^{2} + 10 x + 25

= \frac{2 ( x ^{2} + 10 x + 25 )}{x ^{4} + 4 x ^{2} + 4}

Expand

2 (x^{2} + 10 x + 25) : 2 x^{2} + 20 x + 50

= \frac{2 x ^{2} + 20 x + 50}{x ^{4} + 4 x ^{2} + 4}

\frac{15 x ^{2} + 24 x - 25}{( 5 x + 4 ) ^{2}}

\frac{( x + 6 ) ( x + 2 )}{( x - 3 ) ( x - 2 )}

4 (e^{3 x + 1} + \frac{7}{x}) + ln (3 (e^{3 x + 1} + \frac{7}{x}) + 2)

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

\frac{22 ( 29 x - 144 )}{3}

What is expand (2(x+5)^2)/((x^2+2)^2) ?
The solution to expand (2(x+5)^2)/((x^2+2)^2) is (2x^2+20x+50)/(x^4+4x^2+4)