Question

X^2+7x+10/x-2÷x^2-25/4x-8​

Answer 1

`(x^2+7x+10)/(x-2)/ (x^2-25)/(4x-8)=(4x+8)/(x-5)`

Explanation:

Given:

The expression to simplify is given as:

`(x^2+7x+10)/(x-2)/ (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:

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

Therefore, the given expression is simplified to
`(4x+8)/(x-5)`