Question

Which of the following is the product of the rational expressions shown below? 7x/x-4•x/x+7

Answer 1

The product of the rational expressions$\dfrac{7x}{x-4}.\dfrac{x}{x+7} = \dfrac{7x^2}{x^2+3x-28}$.

Step-by-step explanation:

We have,

$\dfrac{7x}{x-4}.\dfrac{x}{x+7}$

To find, the product of the rational expressions $\dfrac{7x}{x-4}.\dfrac{x}{x+7}$ = ?

∴ $\dfrac{7x}{x-4}.\dfrac{x}{x+7}$

= $\dfrac{7x.x}{(x-4)(x+7)}$

= $\dfrac{7x^2}{(x(x+7)-4(x+7)}$

= $\dfrac{7x^2}{x^2+7x-4x-28}$

= $\dfrac{7x^2}{x^2+3x-28}$

Thus, the product of the rational expressions $\dfrac{7x}{x-4}.\dfrac{x}{x+7} = \dfrac{7x^2}{x^2+3x-28}$.