Question

Solve the following equation:
(-3e^2x)/(x^4) + (2e^2x)/(x^3) = 0
PLease help, I have no idea...

Answer 1

\[\frac{ -3e ^{2x}}{ x^4 }+\frac{ 2e^{2x} }{x^3 }=0\]
For your convenience.

Answer 2

well first you need a common denominator

multiply the 2nd fraction by x and you get
\[\frac{-3e^{2x}}{x^4} + \frac{2xe^{2x}}{x^4} = 0\]

now factor the factor the numerator

\[\frac{e^{2x}(2x -3)}{x^4} = 0\]

so for the equation to equal zero, the the numerator must be zero so

\[e^{2x}(2x - 3) = 0\]

you need to know that the exponential will never be zero.

\[e^{2x} \neq 0\]

so the only way to get a zero numerator is to let

2x - 3 = 0

find the value of x, that makes it true...?

hope it helps

Answer 3

Thank you so much! I just forgot to take out the e^2x which made things really hard for me...