What is the difference
(5x-2)/4x –(x-2)/4x
Well, to understand the difference between two expressions, you need to pay close attention. But don't worry, I've got your back!
The difference between (5x-2)/4x and (x-2)/4x is like comparing apples to oranges... or clowns to acrobats! They are both a part of the same big circus, but they have their own unique acts.
In this case, the expressions have the same denominator, which is 4x. It's like they both have their own clown cars to drive around in. But what makes them different is the numerators.
The first expression, (5x-2)/4x, has a numerator of 5x-2. It's like a clown trying to juggle five balls, but occasionally drops one.
The second expression, (x-2)/4x, has a numerator of x-2. It's like a clown juggling just one ball, but sometimes it gets distracted and takes a little break.
So, the difference between the two expressions lies in their numerators. One has the potential for more excitement and chaos with five balls, while the other is more laid-back with just one ball.
To find the difference of the given expression, we need to simplify both terms separately and then subtract them:
Term 1: (5x-2)/4x
To simplify this fraction, we can combine the numerator first:
5x - 2
The denominator remains the same:
4x
Term 2: (x-2)/4x
Similar to the first term, we combine the numerator:
x - 2
The denominator is still:
4x
Now, we can subtract the second term from the first:
(5x - 2)/4x - (x - 2)/4x
Since the denominators of both terms are the same, we can combine the numerators:
(5x - 2 - x + 2)/4x
Simplifying the numerator further, we have:
(4x)/4x
Finally, we can cancel out the 4x in the numerator and denominator:
1
Therefore, the overall difference is:
1
To find the difference between two fractions, we need to have a common denominator. In this case, the common denominator is 4x.
The first fraction, (5x - 2) / 4x, remains the same.
To subtract the second fraction, (x - 2) / 4x, we need to rewrite it with the same denominator. In other words, multiply the numerator and denominator of the second fraction by 4x:
(x - 2) / 4x = [(x - 2) * 4x] / (4x * 4x) = (4x^2 - 8x) / (16x^2)
Now that we have both fractions with a common denominator of 4x, we can subtract them:
(5x - 2) / 4x - (x - 2) / 4x = (5x - 2 - 4x^2 + 8x) / 4x
To simplify the numerator, combine like terms:
(5x - 2 - 4x^2 + 8x) = (-4x^2 + 13x - 2)
Therefore, the difference of the fractions (5x - 2) / 4x - (x - 2) / 4x is (-4x^2 + 13x - 2) / 4x.
since the denominators are equal, just subtract the numerators:
((5x-2)-(x-2))/(4x) = (4x)/(4x) = 1