SOLUTION: i need so much help with my math hmwk. Right now I am trying to solve the following simplfy x/2x-3 - 1/x=2 Im stuck & iam terrible at math. can u help me solve this

Algebra ->  Rational-functions -> SOLUTION: i need so much help with my math hmwk. Right now I am trying to solve the following simplfy x/2x-3 - 1/x=2 Im stuck & iam terrible at math. can u help me solve this       Log On


   

Question 221296: i need so much help with my math hmwk. Right now I am trying to solve the following
simplfy
x/2x-3 - 1/x=2
Im stuck & iam terrible at math. can u help me solve this

Found 3 solutions by Alan3354, RAY100, drj:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x/2x-3 - 1/x=2
------------------
x%2F%282x-3%29+-+1%2Fx+=+2
You have to combine the 2 terms on the left. Find a common denominator.
A common DEN can always be found by multiplying the DENs. It might not be the Least CD, but it will give the same answer.
(2x-3)*x = 2x^2 - 3x = DEN
------------
x/(2x-3) = x^2/DEN
1 = (x^2-3x)/DEN
Add those
--> (2x^2 - 3x)/DEN
%282x%5E2+-2x%29%2FDEN+=+2
Multiply thru by DEN
2x%5E2+-+2x+=+2%282x%5E2+-+3x%29
2x%5E2+-+2x+=+4x%5E2+-+6x
2x%5E2+-+4x+=+0
x%5E2+-+2x+=+0
x(x-2) = 0
x = 0
x = 2


Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
x/(2x-3) - (1/x) = 2
.
Use LCD = x(2x-3)
.
{x(x) - 1(2x-3)}/x(2x-3) = 2,,,,,,,,cross multiply
.
x^2 -2x +3 = x(2x-3)2 = 4x^2 -6x
.
0= 3x^2 -4x -3
.
using quadratic eqn to solve
.
a=3,,,,,b= -4,,,,,c= -3
.
x= [ -(-4) +/- sqrt{(-4)^2 -4(3)(-3)]/2(3)
.
x= [ 4 +/- sqrt{ 16 +36} ] /6
.
x= [ 4 +/- sqrt {52} ] /6
.
x= [ 4 +/- 7.21] /6
.
x= 1.87,,,-.535
.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
I need so much help with my math hmwk. Right now I am trying to solve the following

simplfy

x%2F%282x-3%29-1%2Fx=2

Step 1. Multiply x(2x-3) to both sides of equation get rid of fractions

x%282x-3%29x%2F%282x-3%29-x%282x-3%29%2Fx=2x%282x-3%29

x%5E2-%282x-3%29=4x%5E2-6x

x%5E2-2x%2B6=4x%5E2-6x

Step 2. Subtract x%5E2 from both sides of the equation

x%5E2-2x%2B6-x%5E2=4x%5E2-6x-x%5E2

-2x%2B6=3x%5E2-6x

Step 3. Add 2x-6 to both sides of the equation

-2x%2B6%2B2x-6x=3x%5E2-6x%2B2x-6]

0=3x%5E2-4x-6

Step 4. Use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=3, b=-4 and c=-6

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%2B-6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A3%2A-6=88.

Discriminant d=88 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+88+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+88+%29%29%2F2%5C3+=+2.23013858660781
x%5B2%5D+=+%28-%28-4%29-sqrt%28+88+%29%29%2F2%5C3+=+-0.896805253274477

Quadratic expression 3x%5E2%2B-4x%2B-6 can be factored:
3x%5E2%2B-4x%2B-6+=+3%28x-2.23013858660781%29%2A%28x--0.896805253274477%29
Again, the answer is: 2.23013858660781, -0.896805253274477. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-6+%29



I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J