Question

How do you solve rational equations?
1/2+1/4=1/x
I need someone to explain it to me.

Answer 1

add up on the left
\[\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\]
start with
\[\frac{3}{4}=\frac{1}{x}\] then flip both sides to solve for \(x\)

Answer 2

Another method is to multiply both sides by the LCD. The LCD of 2, 4, and x is 4x:
\[(4x)(\frac{ 1 }{ 2 } + \frac{ 1 }{ 4 }) = (4x)(\frac{ 1 }{ x })\]
\[(4x)(\frac{ 1 }{ 2 }) + (4x)(\frac{ 1 }{ 4 }) = (4x)(\frac{ 1 }{ x })\]
2x + x = 4
Now continue from here.