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-

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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-      Log On


   

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) About Me  (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 x-4 and forgot the 5. So you should have


5%28x-2%29%2B2%2Ahighlight%285%29%2A%28x-4%29=%282x%2B3%29%28x-4%29


5%28x-2%29%2B10%28x-4%29=%282x%2B3%29%28x-4%29 Multiply


5x-10%2B10x-40=%282x%2B3%29%28x-4%29 Distribute


5x-10%2B10x-40=2x%5E2-5x-12 Foil


5x-10%2B10x-40-2x%5E2%2B5x%2B12=0 Get all terms to one side



-2x%5E2%2B20x-38=0 Combine like terms


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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

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



So lets solve -2%2Ax%5E2%2B20%2Ax-38=0 ( notice a=-2, b=20, and c=-38)




x+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-2%2A-38+%29%29%2F%282%2A-2%29 Plug in a=-2, b=20, and c=-38



x+=+%28-20+%2B-+sqrt%28+400-4%2A-2%2A-38+%29%29%2F%282%2A-2%29 Square 20 to get 400



x+=+%28-20+%2B-+sqrt%28+400%2B-304+%29%29%2F%282%2A-2%29 Multiply -4%2A-38%2A-2 to get -304



x+=+%28-20+%2B-+sqrt%28+96+%29%29%2F%282%2A-2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-20+%2B-+4%2Asqrt%286%29%29%2F%282%2A-2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-20+%2B-+4%2Asqrt%286%29%29%2F-4 Multiply 2 and -2 to get -4

So now the expression breaks down into two parts

x+=+%28-20+%2B+4%2Asqrt%286%29%29%2F-4 or x+=+%28-20+-+4%2Asqrt%286%29%29%2F-4


Now break up the fraction


x=-20%2F-4%2B4%2Asqrt%286%29%2F-4 or x=-20%2F-4-4%2Asqrt%286%29%2F-4


Simplify


x=5-sqrt%286%29 or x=5%2Bsqrt%286%29




So our solutions are:

x=5-sqrt%286%29 or x=5%2Bsqrt%286%29