SOLUTION: Find the root(s) of x-2/x-4 + 2= 2x+3/5 Can someone please tell me why I lost marks :( I Did : 5(x-2)+2(x-4)=(2x+3)(x-4) 5x-10+2x-8=2x^2-8x+3x-12 7x-18=2x62-

Question 118765: Find the root(s) of x-2/x-4 + 2= 2x+3/5
Can someone please tell me why I lost marks :(
I Did : 5(x-2)+2(x-4)=(2x+3)(x-4)
5x-10+2x-8=2x^2-8x+3x-12
7x-18=2x62-5x-12
7x-18+-2x^2+5x+12=0
12x-6+-2x^2=0
x^2+-6x+3=0
Then I used the quadratic formula and got:
x=6+-2sqrt6/2
x=3=-sqrt6

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You made a mistake in your first step. Remember, the LCD is 5(x-4). You multiplied the second term 2 by only the expression and forgot the 5. So you should have

Multiply

Distribute

Foil

Get all terms to one side

Combine like terms

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-2, b=20, and c=-38

Square 20 to get 400

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -2 to get -4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So our solutions are:

or

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