how would you solve x^(5/2)(x^(1/2)- 1/x^(1/2))
I would rewrite it as
x^3 -x^2
Since you have not written an equation, there is nothing to solve. Did you omit an " = 0 " at the end?
To solve the expression x^(5/2)(x^(1/2) - 1/x^(1/2)), we can simplify it step by step:
1. Start by simplifying the expression within the parentheses. We have x^(1/2) - 1/x^(1/2).
To simplify this, we need to find a common denominator. The common denominator of x^(1/2) and 1/x^(1/2) is x^(1/2).
So, we rewrite the expression as ((x^(1/2)) * (x^(1/2))/(x^(1/2))) - (1/x^(1/2)).
This becomes (x - 1)/(x^(1/2)).
2. Now, we can substitute this simplified expression back into the original equation:
x^(5/2) * (x^(1/2) - 1/x^(1/2)) = x^(5/2) * ((x - 1)/(x^(1/2))).
3. Next, simplify the expression further by using the exponent rule: a^(m/n) = (n√a)^m.
Applying this rule to x^(5/2), we have (x^(2/2) * x^(1/2)) * ((x - 1)/(x^(1/2))).
Simplifying further, we have (x * x^(1/2)) * ((x - 1)/(x^(1/2))).
4. Now, we can simplify the expression by canceling x^(1/2) terms.
x * x^(1/2) is equal to x^(1 + 1/2), which simplifies to x^(3/2).
Similarly, x^(1/2) / x^(1/2) cancels out, leaving us with (x - 1).
5. Combining the simplified terms, we get the final expression: x^(3/2) * (x - 1).
Therefore, the solution to the expression x^(5/2)(x^(1/2) - 1/x^(1/2)) is x^(3/2) * (x - 1).