Question

X^2+7x+10/x-2÷x^2-25/4x-8​

Answer 1

Answer:

$\frac{x^2+7x+10}{x-2}\div \frac{x^2-25}{4x-8}=\frac{4x+8}{x-5}$

Step-by-step explanation:

Given:

The expression to simplify is given as:

$\frac{x^2+7x+10}{x-2}\div \frac{x^2-25}{4x-8}$

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:

$=\frac{x^2+7x+10}{x-2}\times \frac{4x-8}{x^2-25}\\\\\textrm{Factoring all the given expressions, we get:}\\\\=\frac{(x+2)(x+5)}{(x-2)}\times \frac{4(x-2)}{(x+5)(x-5)}\\\\=\frac{(x+2)(x+5)4(x-2)}{(x-2)(x+5)(x-5)}\\\\\textrm{Cancelling like terms,we get:}\\\\=\frac{4(x+2)}{x-5}=\frac{4x+8}{x-5}$

Therefore, the given expression is simplified to $\frac{4x+8}{x-5}$