What is the solution to the rational equation x / 2x + 1 + 1 / 4 = 2 / 2x + 1?
is the equaton suppose to look like this
(x/2x) + 1 + 1/4 = (2/2x) + 1 ?
if it is then what you do is simplify ffirst
(x/2x) = 1/2 cause x cancel
(1/2) + 1 +(1/4) = (2/2x) + 1
and (2/2x) =(1/x)
(1/2) + 1 + (1/4) = (1/x) + 1
1 + (3/4) = (1/x) + 1
subtract 1 from both side
(3/4) = (1/x) and then multiply x to get rid of it from the denominator
(3/4)x = 1
x= (4/3)
To find the solution to the rational equation, we will first need to simplify it. The given equation is:
x / (2x + 1) + 1/4 = 2 / (2x + 1)
To simplify, let's find a common denominator for the fractions on both sides of the equation. The common denominator here is 4(2x + 1), so we need to multiply each fraction by the appropriate factors to obtain this common denominator.
So, multiplying each term by 4(2x + 1), the equation becomes:
4(2x + 1) * (x / (2x + 1)) + 4(2x + 1) * (1/4) = 4(2x + 1) * (2 / (2x + 1))
Simplifying this further:
4x + 4 = 8
Now, let's solve for x:
4x + 4 = 8
Subtract 4 from both sides of the equation:
4x = 4
Divide both sides of the equation by 4:
x = 1
Therefore, the solution to the given rational equation is x = 1.