Question 420551
{{{(x+1)/(x-2)=(x-3)/x}}}
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.<br>
Since your equation is a proportion we can use cross-multiplying:
{{{(x+1)(x) = (x-2)(x-3)}}}
Multiplying out each side we get:
{{{x^2+x = x^2-5x+6}}}
This appears to be a quadratic equation. But if we subtract {{{x^2}}} 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<br>
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:
{{{(x+1)/(x-2)=(x-3)/x}}}
Checking x = 1:
{{{((1)+1)/((1)-2)=((1)-3)/(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 <i>no</i> 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.<br>
Since the solution passed the check, the solution to your equation is x = 1.