SOLUTION: Hello, I would like to know how could I solve the following expression: {{{(2x*sqrt(x)-(x^2)/(2*sqrt(x)))/x}}} I know that the answer is {{{(3*sqrt(x))/(2)}}} because it app

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, I would like to know how could I solve the following expression: {{{(2x*sqrt(x)-(x^2)/(2*sqrt(x)))/x}}} I know that the answer is {{{(3*sqrt(x))/(2)}}} because it app      Log On


   



Question 785754: Hello, I would like to know how could I solve the following expression:
%282x%2Asqrt%28x%29-%28x%5E2%29%2F%282%2Asqrt%28x%29%29%29%2Fx
I know that the answer is %283%2Asqrt%28x%29%29%2F%282%29 because it appears on page 5 of this math guide from college (sorry for any grammar errors or misspellings. I am from Argentina and my first language is Spanish, not English), but I need to know the procedure, in case I am presented with a similar problem in any of the upcoming Maths exams.
Many thanks in advance for any help you could provide.
P.S: I tried to find the right section to post this math problem but I am not entirely sure this one belongs here. In case it doesn't, please move it to the right section. Thanks.

Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Find a common denominator to add like fractions on the top. Remember that 2x%2Asqrt%28x%29%2F1 Multiply both denominators by 2%2Asqrt%28x%29, which is the Least Common Denominator. Remember that x%5Ea+%2A+x%5Eb+=+x%5E%28a%2Bb%29 and for division, it's the same but subtract the exponents.


%28%282x%2Asqrt%28x%29%2A2sqrt%28x%29+-+x%5E2%29%2F%282%2Asqrt%28x%29%29%29%2Fx


The denominator on top drops to the denominator.


Remember to add the exponents when multiplying a base to different exponents. The square root of something is something to the 1/2 power.


%284x%5E2+-+x%5E2%29%2F2x%5E%283%2F2%29=+%283x%5E2%29%2F2x%5E%283%2F2%29. Combine the x terms by subtracting the exponent in the denominator from the exponent in the numerator. 2-3/2 - 1/2


3x%5E%281%2F2%29%2F2+=+3sqrt%28x%29%2F2