Answer:
z = -1
Step-by-step explanation:
Given the equation;
[tex]\frac{1}{z+1} +\frac{5}{z+5} = \frac{4}{z^2+6z+5}\\[/tex]\
Find the LCM
[tex]\frac{1(z+5)+5(z+1)}{z^2+6x+5} = \frac{4}{z^2+6z+5}\\\\1(z+5)+5(z+1) = 4\\Expand\\z+5+5z+5 = 4\\6z+10 = 4\\6z = 4 -10\\6z = -6\\z = -6/6\\z = -1\\[/tex]
Hence the value of z that satisfies the equation is -1
