SOLUTION: Hi I need help with Rational Equations. It says to solve the equation choosing a method. 39. 1/4+4/x=1/x 40. -3x/(x+1)=-2/(x-1) 41. x/6-1/x=1/6 Im using Algebra 1 Conc

Question 75286: Hi I need help with Rational Equations. It says to solve the equation choosing a method.
39. 1/4+4/x=1/x
40. -3x/(x+1)=-2/(x-1)
41. x/6-1/x=1/6
Im using Algebra 1 Concept and Skills By McDougal Chapter 11.7. If you can do these problems and explain them to me I'd be very grateful. Thank You!
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
With rational expressions, try to get rid of the denominator by finding the LCD.
39. 1/4+4/x=1/x [LCD = 4x]
4x(1/4+4/x=1/x) [multiply each term by the LCD and cancel wherever possible]
4x/4+(4)(4x)/x=4x/x
x+16=4
x+16-4=4-4
x+12=0
[solve for x]
x=-12
.
Check by plugging x=-12 back into the original equation:
1/4+4/(-12)=1/(-12)
4/-48=-1/12
-1/12=-1/12 [checks out]
.
.
.
40. -3x/(x+1)=-2/(x-1)
LCD=(x+1)(x-1)
(x+1)(x-1)[-3x/(x+1)=-2/(x-1)]
(-3x)(x-1)=(-2)(x+1) [simplify]
-3x^2+3x=-2x-2
-3x^2+3x+2x+2=0
-3x^2+5x+2=0
Use the quadratic formula to solve for zero:
x= 2 or x=-1/3
.

41. x/6-1/x=1/6
LCD=6x
6x(x/6-1/x=1/6 )
(6x)(x)/6-(6x)/x=(6x)/6
x^2-6=x
x^2-x-6=0
Use the quadratic formula to solve for x:
x=3 or x=-2

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