SOLUTION: Dear tutors, It would help me greatly if you could explain to me how to solve these two equations. I already have the answer but I do not know how to get it. So if you could show

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Dear tutors, It would help me greatly if you could explain to me how to solve these two equations. I already have the answer but I do not know how to get it. So if you could show      Log On


   

Question 889756: Dear tutors,
It would help me greatly if you could explain to me how to solve these two equations. I already have the answer but I do not know how to get it. So if you could show me the calculation that leads to the asnwer, that would be great.
Question: 2x^2/ cube root of 4x
The answer should be = x cube root of 2x^2
Question: (x/x^2-x-6)-(2/x-3) = 3

Thank you so much for you help,
kate B.
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2F%284x%29%5E%281%2F3%29=%282%2F4%5E%281%2F3%29%29x%5E%282-%281%2F3%29%29

2x%5E2%2F%284x%29%5E%281%2F3%29=%282%5E%281%2F3%29%29x%5E%285%2F3%29%29
2x%5E2%2F%284x%29%5E%281%2F3%29=%282%5E%281%2F3%29%29x%5E%285%2F3%29
2x%5E2%2F%284x%29%5E%281%2F3%29=2%5E%281%2F3%29x%5E%283%2F3%29x%5E%282%2F3%29
highlight%282x%5E2%2F%284x%29%5E%281%2F3%29=x%2A%282x%5E2%29%5E%281%2F3%29%29
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.
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Find the common denominator, x%5E2-x-6=%28x-3%29%28x%2B2%29

%28x-2x-4%29%2F%28x-3%29%28x%2B2%29=%283x%5E2-3x-18%29%2F%28%28x-3%29%28x%2B2%29%29
%283x%5E2%2B2x-14%29%2F%28%28x-3%29%28x%2B2%29%29=0
Find when the numerator equals zero.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A3%2A%28-14%29+%29%29%2F%282%2A3%29+
x+=+%28-2+%2B-+sqrt%28+4-4%2A3%2A%28-14%29+%29%29%2F%286%29+
x+=+%28-2+%2B-+2%2Asqrt%28+1%2B42+%29%29%2F%286%29+
x+=+%28-2+%2B-+2%2Asqrt%28+43+%29%29%2F6
highlight%28x+=+%28-1+%2B-+sqrt%28+43+%29%29%2F3+%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1. 2x^2 / (4x)^(1/3) =
multiply both the numerator and denominator by (4x)^(2/3)
(2x^2) * (4x)^(2/3)) / 4x =
cancel x and 2 from numerator and denominator
x * (4x)^(2/3)) / 2 =
square 4x
x * (8*2*x^2)^(1/3) / 2 =
note that cube root of 8 is 2
2x * (x^2)^(1/3) / 2 =
cancel 2 from numerator and denominator
x * (x^2)^(1/3) = x cube root of 2x^2
2. (x/x^2-x-6)-(2/x-3) = 3
factor denominator of first fraction
(x / ((x-3)*(x+2)) - (2/(x-3)) = 3
common denominator of both fractions is (x-3)*(x+2)
(x - (2*(x+2)) / ((x-3)*(x+2)) = 3
expand the numerator
(x -2x -4) / ((x-3)*(x+2)) = 3
combine like terms
(-x -4) = 3*(x-3)*(x+2)
-x -4 = 3 * (x^2-x-6)
-x -4 = 3x^2 -3x -18
3x^2 -2x -14 = 0
use quadratic formula
x = (2 + square root((-2)^2 -4*3*(-14)))/(2*3) = 2.519146175 is approx 2.52
x = (2 - square root((-2)^2 -4*3*(-14)))/(2*3) = −1.852479508 is approx -1.85
now check our answers with original equation
(2.52 / ((2.52)^2 -(2.52) -6) - (2 / ((2.52) / (2.52 - 3))) = 3
3.005162242 is approx 3
(-1.85 / ((-1.85)^2 -(-1.85) -6) - (-1.85 / ((-1.85 -3))) = 3
2.95532646 is approx 3
our answers of x = 2.52 or -1.85 check with original equation