Step-by-step explanation:
We have,
[tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
To find, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex] = ?
∴ [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
= [tex]\dfrac{7x.x}{(x-4)(x+7)}[/tex]
= [tex]\dfrac{7x^2}{(x(x+7)-4(x+7)}[/tex]
= [tex]\dfrac{7x^2}{x^2+7x-4x-28}[/tex]
= [tex]\dfrac{7x^2}{x^2+3x-28}[/tex]
Thus, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex] = [tex]\dfrac{7x^2}{x^2+3x-28}[/tex]
