What is expand (4(x-1)^2)/(x^2-4x+5) ?

The solution to expand (4(x-1)^2)/(x^2-4x+5) is (4x^2-8x+4)/(x^2-4x+5)

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expand (4(x-1)^2)/(x^2-4x+5)

expand

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

\frac{4 x ^{2} - 8 x + 4}{x ^{2} - 4 x + 5}

Solution steps

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

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

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

Expand

4 (x^{2} - 2 x + 1) : 4 x^{2} - 8 x + 4

= \frac{4 x ^{2} - 8 x + 4}{x ^{2} - 4 x + 5}

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

\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}}

What is expand (4(x-1)^2)/(x^2-4x+5) ?
The solution to expand (4(x-1)^2)/(x^2-4x+5) is (4x^2-8x+4)/(x^2-4x+5)