Solve frac{(1+x^{2})^2(9)-6x(9)(1+x^2)(6x)}{(1+x^2)^4}

$$\frac { ( 1 + x ^ { 2 } ) ^ { 2 } ( 9 ) - 6 x ( 9 ) ( 1 + x ^ { 2 } ) ( 6 x ) } { ( 1 + x ^ { 2 } ) ^ { 4 } }$$

Evaluate

$$\frac{9\left(1-35x^{2}\right)}{\left(x^{2}+1\right)^{3}}$$

Short Solution Steps

Multiply x and x to get x^{2}.

$$\frac{\left(1+x^{2}\right)^{2}\times 9-6x^{2}\times 9\left(1+x^{2}\right)\times 6}{\left(1+x^{2}\right)^{4}}$$

Multiply 6 and 9 to get 54.

$$\frac{\left(1+x^{2}\right)^{2}\times 9-54x^{2}\left(1+x^{2}\right)\times 6}{\left(1+x^{2}\right)^{4}}$$

Multiply 54 and 6 to get 324.

$$\frac{\left(1+x^{2}\right)^{2}\times 9-324x^{2}\left(1+x^{2}\right)}{\left(1+x^{2}\right)^{4}}$$

Factor the expressions that are not already factored.

$$\frac{9\left(-35x^{2}+1\right)\left(x^{2}+1\right)}{\left(x^{2}+1\right)^{4}}$$

Cancel out x^{2}+1 in both numerator and denominator.

$$\frac{9\left(-35x^{2}+1\right)}{\left(x^{2}+1\right)^{3}}$$

Expand the expression.

$$\frac{-315x^{2}+9}{x^{6}+3x^{4}+3x^{2}+1}$$

Expand

$$-\frac{9\left(35x^{2}-1\right)}{\left(x^{2}+1\right)^{3}}$$

Short Solution Steps

Multiply x and x to get x^{2}.

$$\frac{\left(1+x^{2}\right)^{2}\times 9-6x^{2}\times 9\left(1+x^{2}\right)\times 6}{\left(1+x^{2}\right)^{4}}$$

Multiply 6 and 9 to get 54.

$$\frac{\left(1+x^{2}\right)^{2}\times 9-54x^{2}\left(1+x^{2}\right)\times 6}{\left(1+x^{2}\right)^{4}}$$

Multiply 54 and 6 to get 324.

$$\frac{\left(1+x^{2}\right)^{2}\times 9-324x^{2}\left(1+x^{2}\right)}{\left(1+x^{2}\right)^{4}}$$

Factor the expressions that are not already factored.

$$\frac{9\left(-35x^{2}+1\right)\left(x^{2}+1\right)}{\left(x^{2}+1\right)^{4}}$$

Cancel out x^{2}+1 in both numerator and denominator.

$$\frac{9\left(-35x^{2}+1\right)}{\left(x^{2}+1\right)^{3}}$$

Expand the expression.

$$\frac{-315x^{2}+9}{x^{6}+3x^{4}+3x^{2}+1}$$