What is (x-1)/(2x^2+4x+2)*((x+1)^2)/(x-1) ?

The solution to (x-1)/(2x^2+4x+2)*((x+1)^2)/(x-1) is 1/2

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simplify (x-1)/(2x^2+4x+2)*((x+1)^2)/(x-1)

simplify

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

\frac{1}{2}

Solution steps

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

Cross-cancel common factor:

x - 1

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

Factor

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

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

Cancel the common factor:

(x + 1)^{2}

= \frac{1}{2}

(5 x - 9)^{2}

\frac{10 a ^{2} b ^{3} c}{80 ( a ^{3} - a ^{2} b )}

\frac{n ^{2}}{9} + 2 mn + 9 m^{2}

x \frac{1}{3}

\frac{6 ( 2 a - 4 c ) - 6 ( 6 a - 4 b ) + 3 ( 4 b - 8 c )}{4}

What is (x-1)/(2x^2+4x+2)*((x+1)^2)/(x-1) ?
The solution to (x-1)/(2x^2+4x+2)*((x+1)^2)/(x-1) is 1/2