SOLUTION: {{{(x-2)/(x-3) = (x-1)/(x+1)}}}

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Question 36749: %28x-2%29%2F%28x-3%29+=+%28x-1%29%2F%28x%2B1%29
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x-2%29%2F%28x-3%29+=+%28x-1%29%2F%28x%2B1%29+
Cross multiply
+%28x-2%29%28x%2B1%29=%28x-3%29%28x-1%29+
FOIL both sides
+x%5E2+-1x+-2+=+x%5E2+-4x+%2B3+
the x^2 cancel each other out since they are of the same coefficient and sign
+-1x+-2+=+-4x+%2B3+
Add 4x and 2 to both sides
+3x+=+5+
divide by 3
+x=+5%2F3+
Plug this into each of the denominators.
+%285%2F3%29+-+3+ and +%285%2F3%29+%2B+1+
+%285%2F3%29+-+%289%2F3%29+ and +%285%2F3%29+%2B+%283%2F3%29+
+%28-4%2F3%29+ and +%288%2F3%29+
Neither of these comes out to be zero, so both are solutions to the rational equation