To make [tex]\( c \)[/tex] the subject of the formula from the given equation [tex]\( 5a = \frac{b - 2c}{bc} \)[/tex], follow these steps:
1. Clear the fraction: To eliminate the fraction, multiply both sides of the equation by [tex]\( bc \)[/tex]:
[tex]\[
5a \cdot bc = b - 2c
\][/tex]
This simplifies to:
[tex]\[
5abc = b - 2c
\][/tex]
2. Rearrange the equation: Move all terms involving [tex]\( c \)[/tex] to one side of the equation:
[tex]\[
5abc + 2c = b
\][/tex]
3. Factor out [tex]\( c \)[/tex]: Extract [tex]\( c \)[/tex] as a common factor from the left side:
[tex]\[
c(5ab + 2) = b
\][/tex]
4. Isolate [tex]\( c \)[/tex]: Finally, divide both sides by [tex]\( (5ab + 2) \)[/tex] to solve for [tex]\( c \)[/tex]:
[tex]\[
c = \frac{b}{5ab + 2}
\][/tex]
Thus, the formula for [tex]\( c \)[/tex] in terms of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] is:
[tex]\[
c = \frac{b}{5ab + 2}
\][/tex]
