Rewrite as equivalent rational expressions with denominator (4y+5)(y−7)(y+8):2y4y2−23y−35,44y2+37y+40.

To rewrite the given expressions with the denominator (4y+5)(y−7)(y+8), we need to factorize the denominators of the given expressions and then multiply by the missing factors to make the denominators equivalent.

1. For the first expression 2y/(4y^2−23y−35):

Factorize the denominator 4y^2−23y−35. This factors to (4y+5)(y-7).

To make this denominator equivalent to (4y+5)(y−7)(y+8), we need to multiply by (y+8)/(y+8).

So, the equivalent expression is [2y(y+8)]/[(4y+5)(y-7)(y+8)].

2. For the second expression 44y^2+37y+40:

This is a polynomial and doesn't have a denominator. To give it the denominator (4y+5)(y−7)(y+8), we simply place it over that denominator.

So, the equivalent expression is (44y^2+37y+40)/[(4y+5)(y−7)(y+8)].