Answer
$\frac{2x-1}{x+1}$.
Work Step by Step
The given expression is
$=\frac{2x+5}{4x^2+8x-5}\cdot \frac{4x^2-4x+1}{x+1}$
Factor $4x^2+8x-5$.
Rewrite the middle term $8x$ as $10x-2x$.
$=4x^2+10x-2x-5$
Group terms.
$=(4x^2+10x)+(-2x-5)$
Factor each term.
$=2x(2x+5)-1(2x+5)$
Factor out $(2x+5)$.
$=(2x+5)(2x-1)$
Factor $4x^2-4x+1$.
Rewrite the middle term $-4x$ as $-2x-2x$.
$=4x^2-2x-2x+1$
Group terms.
$=(4x^2-2x)+(-2x+1)$
Factor each term.
$=2x(2x-1)-1(2x-1)$
Factor out $(2x-1)$.
$=(2x-1)(2x-1)$
Substitute all factors into the given expression.
$=\frac{2x+5}{(2x+5)(2x-1)}\cdot \frac{(2x-1)(2x-1)}{x+1}$
Cancel common terms.
$=\frac{2x-1}{x+1}$.
