For this case, we must find the value of the variable "x", of the following equation:
[tex]5x = 5-25xz ^ 2[/tex]
We add [tex]25xz ^ 2[/tex] to both sides of the equation:
[tex]5x + 25xz ^ 2 = 5-25xz ^ 2+25xz ^ 2\\5x + 25xz ^ 2 = 5[/tex]
We take 5x common factor on the left side:
[tex]5x (1 + 5z ^ 2) = 5[/tex]
We divide between 5 on both sides of the equation:
[tex]\frac {5x (1 + 5z ^ 2)} {5} = \frac {5} {5}\\x (1 + 5z ^ 2) = 1[/tex]
We divide between[tex](1 + 5z ^ 2)[/tex] on both sides of the equation:
[tex]\frac {x (1 + 5z ^ 2)} {(1 + 5z ^ 2)} = \frac {1} {(1 + 5z ^ 2)}\\x = \frac {1} {(1 + 5z ^ 2)}[/tex]
ANswer:
Option C
