Question

Simplify the expression. $$\frac{4 x^{2}-25}{4 x} \div(2 x-5)$$

Short answer

The simplified answer to the problem is \(\frac{x}{2}\).

Step-by-step solution

Rewrite the division as the multiplication by the reciprocal

Rewrite the expression \(\frac{4 x^{2}-25}{4 x} \div(2 x-5)\) as \(\frac{4 x^{2}-25}{4 x} * \frac{1}{2 x-5}\)

Factor out the numerator and Simplify

Factor out the numerator of the first fraction as \(4(x^2 - 6.25)\). Now the expression becomes: \(\frac{4(x^2 - 6.25)}{4x} * \frac{1}{2x-5}\). Simplify this resulting equation by cancelling out similar terms. By doing this, the equation simplifies to \(\frac{x^2 - 6.25}{x}*\frac{1}{2x-5}\)

Simplify further

Rearrange and factor out the shared terms on the equation \(\frac{x^2 - 6.25}{x}*\frac{1}{2x-5}\). This simplifies the equation to: \(x*\frac{1}{2}\). When simplified, the equation becomes: \(\frac{x}{2}\).