Question 961715
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:
--------------------------------------
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/((x+2)(x+3))= 1/((x+4)(x+5))}}}
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