What is expand ((w+1)/(w-1))^2+3((w+1)/(w-1))+K ?

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

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expand ((w+1)/(w-1))^2+3((w+1)/(w-1))+K

expand

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

K + \frac{4 w ^{2} + 2 w - 2}{w ^{2} - 2 w + 1}

Solution steps

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

Remove parentheses:

(a) = a

= (\frac{w + 1}{w - 1})^{2} + 3 \cdot \frac{w + 1}{w - 1} + K

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

3 \cdot \frac{w + 1}{w - 1} = \frac{3 w + 3}{w - 1}

= \frac{w ^{2} + 2 w + 1}{w ^{2} - 2 w + 1} + \frac{3 w + 3}{w - 1} + K

Factor

w^{2} - 2 w + 1 : (w - 1)^{2}

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

Least Common Multiplier of

(w - 1)^{2}, w - 1 : (w - 1)^{2}

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

(w - 1)^{2} = w^{2} - 2 w + 1

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

Expand

w^{2} + 2 w + 1 + (3 w + 3) (w - 1) : 4 w^{2} + 2 w - 2

= K + \frac{4 w ^{2} + 2 w - 2}{w ^{2} - 2 w + 1}

x (1 + \frac{x}{10})

(y - x + x y cot (x)) d x + x d y

(x - y) (x + y)

\frac{\partial}{\partial x} ((f (x)) (x - 2)^{2})

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

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