SOLUTION: please help me solve this equation (x+1)/(x-2)=(x-3)/x

Question 420551: please help me solve this equation (x+1)/(x-2)=(x-3)/x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

When an equation says that one fraction equals another fraction, it is called a proportion. Proportions are the one and only time you use something called cross-multiplying.

Since your equation is a proportion we can use cross-multiplying:

Multiplying out each side we get:

This appears to be a quadratic equation. But if we subtract from each side we get:
x = -5x + 6
which is not a quadratic equation. To solve this we add 5x to each side:
6x = 6
and divide both sides by 6:
x = 1

When solving equations which have the variable in a denominator, you should check your answer(s). You must make sure that no denominator becomes zero. Use the original equation to check:

Checking x = 1:

We can see already that neither denominator will be zero. (If a denominator had been zero we would have to reject the solution and, since x = 1 was the only solution we came up with, there would be no solution to your equation.) This is the required part of the check. The rest of the check is optional and will tell us if we made a mistake. You are welcome finish the check.

Since the solution passed the check, the solution to your equation is x = 1.
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