What is expand x/((x+1)^2)+2/(x^1) ?

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

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expand x/((x+1)^2)+2/(x^1)

expand

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

\frac{3 x ^{2} + 4 x + 2}{x ^{3} + 2 x ^{2} + x}

Solution steps

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

Apply rule

a^{1} = a

x^{1} = x

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

(x + 1)^{2} = x^{2} + 2 x + 1

= \frac{x}{x ^{2} + 2 x + 1} + \frac{2}{x}

Factor

x^{2} + 2 x + 1 : (x + 1)^{2}

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

Least Common Multiplier of

(x + 1)^{2}, x : x (x + 1)^{2}

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

Expand

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

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

Expand

x^{2} + 2 (x^{2} + 2 x + 1) : 3 x^{2} + 4 x + 2

= \frac{3 x ^{2} + 4 x + 2}{x ^{3} + 2 x ^{2} + x}

2^{39} - 2^{11}

\frac{( - 2 a ^{2} - 1 ) ( 4 a ^{4} - 2 a ^{2} + 1 )}{8}

\frac{i}{( a + bi ) ^{2}}

\frac{2 x ^{3} + 5 x - 1}{( 4 x + 7 ) ^{2} ( x ^{2} + 1 ) ^{3}}

(x^{2} + e^{4 x} - 7)^{2}

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