Question

Simplify 16y^2-25/16y^2-40y+25

Answer 1

$\frac{(4y+5)}{(4y-5)}$

Explanation

$\frac{16y^2-25}{16y^2-40y+25}$

Step 1

numerator:

we have a difference of squares:

$\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \end{gathered}$

then, apply

$\begin{gathered} 16y^2-25= \\ 16y^2-5^2=(4y+5)(4y-5) \end{gathered}$

Step 2

numerator

$\begin{gathered} 16y^2-40y+25 \\ 16y^2-20y-20y+25 \\ common\text{ factor} \\ 4y(4y-5)-5(4y-5) \\ (4y-5)(4y-5) \end{gathered}$

Step 3

now, replace

$\begin{gathered} \frac{16y^2-25}{16y^2-40y+25}=\frac{(4y+5)(4y-5)}{(4y-5)(4y-5)}=\frac{(4y+5)}{(4y-5)} \\ \frac{16y^2-25}{16y^2-40y+25}=\frac{(4y+5)}{(4y-5)} \end{gathered}$

I hope this helps you