Solve f(x)=(x^2+1/x^2-1)(1+2x^2)

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

Evaluate

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

Short Solution Steps

Express \frac{x^{2}+1}{x^{2}-1}\left(1+2x^{2}\right) as a single fraction.

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

Use the distributive property to multiply x^{2}+1 by 1+2x^{2} and combine like terms.

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

Expand

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

Short Solution Steps

Express \frac{x^{2}+1}{x^{2}-1}\left(1+2x^{2}\right) as a single fraction.

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

Use the distributive property to multiply x^{2}+1 by 1+2x^{2} and combine like terms.

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