Can someone please help me with solving this equation (I don't know how to do it with the fractions)
1/3 x1^-2/3 . x2^2/3
--------------------
2/3 x1^1/3 . x2^-1/3
how do I cancel out some of the terms and reduce it down so that Im left with x2 on top and x1 on bottom??
And please explain it because I don't know how to cancel out with fractions.
Thanks xx
Add the fractions
ab * ac = ab+c
it probably doesnt show that well but one is x1 and the other x2 so you can add their fractions
I know this is like 13 years later but I don't understand this problem either and I'm usually great with fractions.
To simplify the given equation, we can start by canceling out common factors between the numerator and denominator. In this case, we can cancel out the factors of x1 and x2.
Let's break down the equation step by step for better understanding:
1/3 x1^-2/3 * x2^2/3
-------------------
2/3 x1^1/3 * x2^-1/3
First, let's focus on the numerator:
1/3 * x1^-2/3 * x2^2/3
Using the rule of adding exponents when multiplying, we can rewrite this as:
(1 * x2^2/3) / (3 * (x1^2/3))
Now let's move on to the denominator:
2/3 * x1^1/3 * x2^-1/3
Using the rule of adding exponents when multiplying, we can rewrite this as:
(2 * x1^1/3) / (3 * (x2^1/3))
Now, let's combine the terms in the numerator and denominator:
((1 * x2^2/3) / (3 * (x1^2/3))) / ((2 * x1^1/3) / (3 * (x2^1/3)))
To divide fractions, we can multiply the numerator by the reciprocal of the denominator. So, we multiply the numerator by (3 * (x2^1/3)) and the denominator by (3 * (x1^2/3)).
((1 * x2^2/3) / (3 * (x1^2/3))) * ((3 * (x2^1/3)) / (2 * x1^1/3))
Note that when multiplying fractions, we can multiply the numerators together and the denominators together.
Simplifying further, we have:
(x2^2/3 * 3 * (x2^1/3)) / (3 * x1^2/3 * 2 * x1^1/3)
Now, we can cancel out common factors:
(x2^2/3 * (x2^1/3)) / (2 * x1^2/3 * x1^1/3)
Using the rule of adding exponents when multiplying, we can rewrite this as:
(x2^(2/3 + 1/3)) / (2 * x1^(2/3 + 1/3))
Simplifying the exponents:
(x2^(3/3)) / (2 * x1^(3/3))
Notice that x2^(3/3) is simply x2^1, and x1^(3/3) is simply x1^1.
So, we end up with:
x2 / (2 * x1)
Therefore, the simplified equation is x2 / (2 * x1).