Answer:
[tex]\frac{x^2+7x+10}{x-2}\div \frac{x^2-25}{4x-8}=\frac{4x+8}{x-5}[/tex]
Step-by-step explanation:
Given:
The expression to simplify is given as:
[tex]\frac{x^2+7x+10}{x-2}\div \frac{x^2-25}{4x-8}[/tex]
The division of two fractions is done by replacing the division sign by multiplication sign and taking the reciprocal of the second fraction. So, the above expression becomes:
[tex]=\frac{x^2+7x+10}{x-2}\times \frac{4x-8}{x^2-25}\\\\\textrm{Factoring all the given expressions, we get:}\\\\=\frac{(x+2)(x+5)}{(x-2)}\times \frac{4(x-2)}{(x+5)(x-5)}\\\\=\frac{(x+2)(x+5)4(x-2)}{(x-2)(x+5)(x-5)}\\\\\textrm{Cancelling like terms,we get:}\\\\=\frac{4(x+2)}{x-5}=\frac{4x+8}{x-5}[/tex]
Therefore, the given expression is simplified to [tex]\frac{4x+8}{x-5}[/tex]
