To solve the equation 8/3e² = 9/e + 4/3e³, you should use like denominators as the special case. Find the least common denominator, multiply each term to eliminate fractions, and solve for 'e'.
When solving the rational equation 8/3e² = 9/e + 4/3e³, the special case that you should use is the one that involves obtaining like denominators for all terms of the equation.
To solve such an equation, you would first identify a common denominator that would allow you to combine the fractions. In this case, that common denominator is 3e³. This choice of common denominator comes from recognizing that each denominator is a power of 'e', and thus, by finding the least common multiple of these powers, you can express all terms with the same denominator.
Multiply each term by the common denominator to eliminate fractions and then combine like terms. Once the equation is simplified, it can be solved for the variable 'e'. It is essential to check for extraneous solutions, especially since rational equations can sometimes lead to them.
Complete Question:
Which special case should you use when solving the rational equation 8/3e² = 9/e + 4/3e³ ?
a.No special case applies.
b.No solution
c.No variables in any of the denominators.
d.Like denominators