What is 2/(1+(x-1)^2(x+3)^2) ?

The solution to 2/(1+(x-1)^2(x+3)^2) is 2/(x^4+4x^3-2x^2-12x+10)

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simplify 2/(1+(x-1)^2(x+3)^2)

simplify

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

\frac{2}{x ^{4} + 4 x ^{3} - 2 x ^{2} - 12 x + 10}

Solution steps

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

Expand

(x - 1)^{2} (x + 3)^{2} : x^{4} + 4 x^{3} - 2 x^{2} - 12 x + 9

= \frac{2}{1 + x ^{4} + 4 x ^{3} - 2 x ^{2} - 12 x + 9}

Simplify

1 + x^{4} + 4 x^{3} - 2 x^{2} - 12 x + 9 : x^{4} + 4 x^{3} - 2 x^{2} - 12 x + 10

= \frac{2}{x ^{4} + 4 x ^{3} - 2 x ^{2} - 12 x + 10}

3 x + 2 x^{2}

2 - 5

4 (x + h)^{2} + 2 (x + h) - 2

x^{3} + x^{2} y

\frac{1}{x} - \frac{1}{sin ( x )}

What is 2/(1+(x-1)^2(x+3)^2) ?
The solution to 2/(1+(x-1)^2(x+3)^2) is 2/(x^4+4x^3-2x^2-12x+10)