SOLUTION: Solve this equation for x with working: (x+3)/(x+5)=(x+1)/(x+2)

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Question 682817: Solve this equation for x with working:
(x+3)/(x+5)=(x+1)/(x+2)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3%29%2F%28x%2B5%29=%28x%2B1%29%2F%28x%2B2%29
You can cross multiply when you have a fraction equal to another, however multiplying both sides by the LCD works every time for rational equations.
The LCD is (x+5)(x+2)

The denominators cancel:
%28x%2B2%29%28x%2B3%29=%28x%2B5%29%28x%2B1%29
Foil and solve:
x%5E2%2B2x%2B3x%2B6=x%5E2%2Bx%2B5x%2B5
x%5E2%2B5x%2B6=x%5E2%2B6x%2B5
-x%5E2%2Bx%5E2%2B5x%2B6=-x%5E2%2Bx%5E2%2B6x%2B5
5x%2B6=6x%2B5
-5x%2B5x%2B6=-5x%2B6x%2B5
6=x%2B5
6-5=x%2B5-5
1=x
highlight%28x=1%29
*Note* Always check and make sure that your answer does not make any denominator 0...that makes fractions undefined. If you had gotten -5 or -2, then there would be no solution.
Happy Calculating.