SOLUTION: Can you please walk me through the steps to solve this problem? (x-1)/(x+3)=(x+2)/(x-4)

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Question 611792: Can you please walk me through the steps to solve this problem? (x-1)/(x+3)=(x+2)/(x-4)
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please walk me through the steps to solve this problem?
x-1)/(x+3)=(x+2)/(x-4)
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Cross-multiply:
(x-1)(x-4) = (x+3)(x+2)
Use FOIL on both sides:
x^2-4x-x+4 = x^2 + 2x + 3x + 6
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Simplify:
x^2 -5x +4 = x^2 + 5x + 6
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Simplify:
10x = -2
x = -1/5
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Cheers,
Stan H.
====================

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
++%28x-1%29+%2F+%28x%2B3%29+=+%28x%2B2%29+%2F+%28x-4%29+
Multiply both sides by +%28+x+%2B+3+%29%2A%28+x+-+4+%29+
Note that when you multiply both sides of any
equation by the same thing, the equation is still
true.

+%28+x+-+4+%29%2A%28+x+-+1+%29+=+%28+x+%2B+3+%29%2A%28+x+%2B+2+%29+
Expand each side
+x%5E2+-+4x+-+x+%2B+4+=+x%5E2+%2B+3x+%2B+2x+%2B+6+
Subtract +x%5E2+ from each side
+-4x+-+x+%2B+4+=+3x+%2B+2x+%2B+6+
Combine like terms
+-5x+%2B+4+=+5x+%2B+6+
Add +5x+ to both sides
+4+=+10x+%2B+6+
Subtract +6+ from both sides
+10x+=+-2+
Divide both sides by +10+
+x+=+-+2%2F10+
+x+=+-1%2F5+ answer
-------------------
You can easily check this. +-2%2F10+=+-.2+
Plug this back into original equation.
++%28x-1%29+%2F+%28x%2B3%29+=+%28x%2B2%29+%2F+%28x-4%29+
++%28-.2-1%29+%2F+%28-.2%2B3%29+=+%28-.2%2B2%29+%2F+%28-.2-4%29+
++%28+-1.2+%29+%2F+%28+2.8+%29+=+%28+1.8%29+%2F+%28+-4.2+%29+
Now do the divisions with a calculator
+-.4285714+=+-.4285714+
OK