SOLUTION: Tutor, Could I get some help with this problem? I am having difficulty solving it. x/5x + 10 + x-3/x+2 = 7/5 Thank you for your help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Tutor, Could I get some help with this problem? I am having difficulty solving it. x/5x + 10 + x-3/x+2 = 7/5 Thank you for your help.      Log On


   

Question 99480: Tutor,
Could I get some help with this problem? I am having difficulty solving it.
x/5x + 10 + x-3/x+2 = 7/5
Thank you for your help.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28%285x+%2B+10%29%29 + %28%28x-3%29%29%2F%28%28x%2B2%29%29 = 7%2F5
:
factor out 5 in the 1st denominator:
x%2F%285%28x+%2B+2%29%29 + %28%28x-3%29%29%2F%28%28x%2B2%29%29 = 7%2F5
:
Multiply equation by 5(x+2), and eliminate the denominators, leaving us with:
x + 5(x-3) = 7(x+2)
:
x + 5x - 15 = 7x + 14
x + 5x - 7x = 14 + 15
-x = +29
x = -29
:
:
Check solution, substitute -29 for x in the original equation:
%28-29%29%2F%28%285%28-29%29+%2B+10%29%29 + %28%28%28-29%29-3%29%29%2F%28%28%28-29%29%2B2%29%29 = 7%2F5
%28-29%29%2F%28%28-145+%2B+10%29%29 + %28%28-32%29%29%2F%28%28-27%29%29 = 7%2F5
%28-29%29%2F%28%28-135%29%29 + %28%28-32%29%29%2F%28%28-27%29%29 = 7%2F5
Check using decimals
+.2148 + 1.1852 = 1.4 which is 7/5