SOLUTION: I sent a problem yesterday and didn't get a response so can somebody please help me step by step with this problem. x+3/x+2- x+4/x+3= x+5/x+4- x+6/x+5. The / means fractions. I rea

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I sent a problem yesterday and didn't get a response so can somebody please help me step by step with this problem. x+3/x+2- x+4/x+3= x+5/x+4- x+6/x+5. The / means fractions. I rea      Log On


   

Question 961715: I sent a problem yesterday and didn't get a response so can somebody please help me step by step with this problem. x+3/x+2- x+4/x+3= x+5/x+4- x+6/x+5. The / means fractions. I really don't understand this problem.
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Volunteer tutors answer questions when they can. You can also pay for an Algebra.com tutor to help you for a fee and that would ensure that you get help when you want it. Now to your problem:
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x+3/x+2- x+4/x+3= x+5/x+4- x+6/x+5
Bring the left side together using the common denominator (x+2)(x+3), and bring the right side together using the common denominator (x+4)(x+5) so you have:
1%2F%28%28x%2B2%29%28x%2B3%29%29=+1%2F%28%28x%2B4%29%28x%2B5%29%29
Take the reciprocal on both sides and you get:
(x+2)(x+3)= (x+4)(x+5)So now we've got two quadratic polynomials:
x^2+5x+6 = x^2+9x+20 Subtract x^2+9x+20 from both sides:
-4x-14 = 0 Factor the left:
-2(2x+7)= 0 Divide both sides by -2, it will simplify our equation:
2x+7= 0 It should be easy for you from here:
2x = -7
x = -7/2 or -3 1/2