Question

Simplify the expression. $$\left(\frac{3 x^{2}}{56}\right)\left(\frac{3}{x}+\frac{5}{x}\right)$$

Short answer

\(\frac{3x}{7}\)

Step-by-step solution

Expand the expression

The expression \(\left(\frac{3 x^{2}}{56}\right)\left(\frac{3}{x}+\frac{5}{x}\right)\) can be expanded by multiplying \(\frac{3 x^{2}}{56}\) by \(\frac{3}{x}\) and \(\frac{5}{x}\). Doing this gives: \[\frac{3 x^{2}}{56} * \frac{3}{x} + \frac{3 x^{2}}{56} * \frac{5}{x}\] which simplifies to \[\frac{9x}{56} + \frac{15x}{56}\].

Simplify the expression

The terms inside the expression have a common fraction \(\frac{x}{56}\) which combines to give \[\frac{24x}{56}\].

Reduce the fraction

To simplify further, the fraction \(\frac{24x}{56}\) can be reduced by dividing the numerator and the denominator by their greatest common divisor, which is 8. This simplification gives: \[\frac{3x}{7}\].