# SOLUTION: I need to figure out how to solve for x in this problem: (x+1)/(x+1) + (5)/(x+2) = (3)/(x+1)

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Question 263727: I need to figure out how to solve for x in this problem:
(x+1)/(x+1) + (5)/(x+2) = (3)/(x+1)

Found 2 solutions by JBarnum, unlockmath:
Answer by JBarnum(2044)   (Show Source):
You can put this solution on YOUR website!
(x+1)/(x+1) + (5)/(x+2) = (3)/(x+1) times every thing by ((x+1)(X+2))
((x+1)(x+2))+((5(x+1))= ((3(X+2)) multiply together
(x^2+3x+2)+(5x+5)=(3x+6) add like terms
x^2 + 8x + 7= 3x + 6 Subtract 3x and 6 from both sides
. -3x - 6 -3x - 6
x^2 +5x+1=0 now u have a quadratic equation
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=21 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.20871215252208, -4.79128784747792. Here's your graph:

Answer by unlockmath(1614)   (Show Source):
You can put this solution on YOUR website!
Hello,
First off let's get rid of the fractions by multiplying each (x+1)(x+2) to get:
(x+1)(x+2) + (5)(x+1) = (3)(x+2) This can be expanded out tobe:
x^2+3x+2+5x+5=3x+6 Now combine terms and subtract 3x and 6 from both sides to get 5:
x^2+5x+1=0
Now apply the quadratic equation: {{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }
x = (-5 +- sqrt(21))/2
There we go!
RJ
www.math-unlock.com