factoring prob?

Question

how to you solve this using factoring??
I am so confused!! please help, explain, thanks

4(x-2) / x-3 + 3/x = -3 / x(x-3)

I know the answers are -3/4, 2 but I can't get to that point!

Answer 1

Ok, first you put all the fractions over the same denominator, or x(x-3). You multiply the numerator by whatever the denominator has to be multiplied by to reach that. So you get
4(x)(x-2)+3(x-3)=-3 (you can just eliminate the denominator once they are all the same)
so you simplify that to
4x^2-5x-6=0
Then you factor that to
(4x+3)(x-2)=0
then you get the two solutions.

Answer 2

YOu need all of your terms to have a common denominator. Since your denominators have X and (X-3) the LCM would be X(X-3) you need to multiply the top and the bottom of the first term by x, the second top and bottom by (x-3) and the last term is already where you want to be. At the end you should have all denominators of X(X-3)

Once all the denominators are the same you can do away with them and you should have. (4xsq -8x) + (3x-9) = -3
Further simplifying gives you
4xsq - 5x - 9 = -3
However you want to be equal to zero so you can use your quadratic equation. Adding three to both sides gives you
4xsq - 5x -6 = 0
Use the quadratic formula (Im assuming you already learned that) and you have your answers.

My answer is better because anyone will tell you that factoring a quadratic where the A value is not one is a pain.

Answer 3

4(x-2) / x-3 + 3/x = -3 / x(x-3) multiply by x ( x - 3 )
4x( x - 2) + 3 ( x - 3 ) = -3

4x^2 - 8 x + 3 x - 9 + 3 = 0

4x^2 - 5 x - 6 = 0

( 4 x + 3 ) ( x - 2 ) = 0
4x + 3 = 0 or x - 2 = 0
4x = -3 or x = 2
x = - 3 / 4

then x = -3/4 or x = 2

Answer 4

4(x -2) / (x - 3) + 3/ x = -3 / x (x - 3)

[4(x - 2) x + 3 (x -3) ] / x( x - 3) = -3 / x (x - 3)

Since the denominator is now same, we can cancel it on both sides and equate the numerators on both sides.

4x^2 - 8x + 3x - 9 = - 3

or

4x^2 - 5x - 6 = 0

The roots of this quadratic equation are;

x1 = 5 + sqrt. (25 + 96) / 8 and x2 = 5 - sqrt.(25 + 96) / 8

x1 = (5 + sqrt.121)/8 = ( 5 + 11) / 8 = 16/8 = 2
and x2 = (5 - 11) / 8 = - 6/8 = -3/4

Answer 5

3x² + 5x + 2 = 0 the midsection time era is + 5x locate the sum of the midsection time era Multiply the 1st time era three times the final time era 2 equals 6 and element aspects of 6 a million x 6 2 x 3. . . .<=. .Use those aspects + 3 and + 2 fulfill the sum of the midsection time era Insert + 3x and + 2x into the equation 3x² + 5x + 2 = 0 Gropup element 3x² + 3x + 2x + 2 = 0 3x(x + a million) + 2(x + a million) = 0 (3x + 2)(x + a million) = 0 - - - - - - - - Roots 3x + 2 = 0 3x + 2 - 2 = 0 - 2 3x = - 2 3x / 3 = - 2 / 3 x = - 2/3 - - - - - - - - Roots x + a million = 0 x + a million - a million = 0 - a million x = - a million - - - - - - - - s-

Answer 6

4(x-2)/(x-3) +3/x = -3/x(x-3)
=> 4x(x-2)+3(x-3)/x(x-3)=-3/x(x-3) [The left hand side has been simplified]
=> 4x^2-8x+3x-9=-3 [The same denominator of both sides have been eliminated]
=>4x^2-5x-6=0
=>4x^2-8x+3x-6=0
=>4x(x-2)+3(x-2)=0
=>(x-2)(4x+3)=0
Therefore either x-2=0 or 4x+3=0
Hence x=2 or -3/4