Solve -4/x*x/2x^2+8div4x/x

$$\frac { - 4 } { x } \times \frac { x } { 2 x ^ { 2 } + 8 } \div \frac { 4 x } { x }$$

Evaluate

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

Short Solution Steps

Multiply \frac{-4}{x} times \frac{x}{2x^{2}+8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-4x}{x\left(2x^{2}+8\right)}}{\frac{4x}{x}}$$

Cancel out x in both numerator and denominator.

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

Cancel out x in both numerator and denominator.

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

Express \frac{\frac{-4}{2x^{2}+8}}{4} as a single fraction.

$$\frac{-4}{\left(2x^{2}+8\right)\times 4}$$

Use the distributive property to multiply 2x^{2}+8 by 4.

$$\frac{-4}{8x^{2}+32}$$

Differentiate w.r.t. x

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