Given:
[tex]\frac{2x^2+x-21}{x^2+2x}\times\frac{8x+16}{x-3}[/tex]
To find: The reduced form
Explanation:
Let us write it as the factored form.
[tex]\begin{gathered} \frac{2x^2+x-21}{x^2+2x}\times\frac{8x+16}{x-3}=\frac{2x^2+7x-6x-21}{x(x^{}+2)}\times\frac{8(x+2)}{x-3} \\ =\frac{x(2x^{}+7)-3(2x+7)}{x(x^{}+2)}\times\frac{8(x+2)}{x-3} \\ =\frac{(x-3)(2x+7)}{x(x^{}+2)}\times\frac{8(x+2)}{x-3} \end{gathered}[/tex]
Simplifying we get,
[tex]\frac{8(2x+7)}{x}[/tex]
Final answer: The simplest form is,
[tex]\frac{8(2x+7)}{x}[/tex]
