The solution for given expression is [tex]\frac{(z + 2y)}{4}[/tex]
Solution:
Given that rational expression is:
[tex]\frac{z^{2}+4 z y+4 y^{2}}{4 z+8 y}[/tex]
Taking "4" as common term from denominator,
[tex]\frac{z^{2}+4 z y+4 y^{2}}{4(z + 2y)}[/tex] ------- eqn 1
Let us use a algebraic identity which is as follows:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
So, [tex]z^{2}+4 z y+4 y^{2}[/tex] can be expressed as:
[tex]z^{2}+4 z y+4 y^{2} = (z + 2y)^2[/tex]
Substitute the above equation in eqn 1,
[tex]\frac{(z + 2y)^2}{4(z + 2y)}[/tex]
Cancelling (z + 2y) in numerator and denominator
[tex]\rightarrow \frac{(z + 2y)}{4}[/tex]
Thus the solution for given expression is [tex]\frac{(z + 2y)}{4}[/tex]
