(8x)/(24x^2)-40xcdot (15x-25)

To simplify the given expression, we can start by factoring out common terms in the numerator and denominator.<br /><br />The numerator is $8x$, and the denominator is $24x^2 - 40x$. We can factor out $8x$ from the denominator:<br /><br />$24x^2 - 40x = 8x(3x - 5)$<br /><br />Now, we can rewrite the expression as:<br /><br />$\frac{8x}{8x(3x - 5)} \cdot (15x - 25)$<br /><br />We can cancel out the common factor of $8x$ in the numerator and denominator:<br /><br />$\frac{1}{3x - 5} \cdot (15x - 25)$<br /><br />Next, we can factor out $5$ from the second term in the product:<br /><br />$15x - 25 = 5(3x - 5)$<br /><br />Now, the expression becomes:<br /><br />$\frac{1}{3x - 5} \cdot 5(3x - 5)$<br /><br />We can cancel out the common factor of $(3x - 5)$ in the numerator and denominator:<br /><br />$5$<br /><br />Therefore, the simplified expression is $5$.