Isolating 'a' in the Equation: (a + b/c)(d  e) = f
This article will guide you through the steps to isolate the variable 'a' in the equation (a + b/c)(d  e) = f. This process involves applying algebraic operations to manipulate the equation and bring 'a' to one side.
Steps to Isolate 'a'

Expand the equation: Begin by expanding the lefthand side of the equation using the distributive property:
ad  ae + bd/c  be/c = f

Combine terms with 'a': Group the terms containing 'a' together:
ad  ae = f  bd/c + be/c

Factor out 'a': Factor out 'a' from the lefthand side:
a(d  e) = f  bd/c + be/c

Isolate 'a': Divide both sides of the equation by (d  e) to isolate 'a':
a = (f  bd/c + be/c) / (d  e)
Final Solution
The isolated variable 'a' is:
a = (f  bd/c + be/c) / (d  e)
This equation expresses 'a' in terms of the other variables, allowing you to calculate its value if you know the values of the other variables.
Note:
 Remember that (d  e) cannot be equal to zero, as division by zero is undefined.
 This solution assumes that all variables are real numbers.