Solve x^2+1/2x*x^2-1/2x

$$\frac{ { x }^{ 2 } +1 }{ 2x } \times \frac{ { x }^{ 2 } -1 }{ 2x }$$

Evaluate

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

Short Solution Steps

Multiply \frac{x^{2}+1}{2x} times \frac{x^{2}-1}{2x} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 2 and 2 to get 4.

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

Consider \left(x^{2}+1\right)\left(x^{2}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Expand

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

Short Solution Steps

Multiply \frac{x^{2}+1}{2x} times \frac{x^{2}-1}{2x} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 2 and 2 to get 4.

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

Consider \left(x^{2}+1\right)\left(x^{2}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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