SOLUTION: Please explain? Give an example of a rational equation for which there is an actual solution and an extraneous solution if you solve the equation using cross products.

Question 450629: Please explain?
Give an example of a rational equation for which there is an actual solution and an extraneous solution if you solve the equation using cross products.
Found 2 solutions by rwm, solver91311:
Answer by rwm(914) (Show Source): You can put this solution on YOUR website!
Watch out for extraneous solutions when solving equations with a variable in the denominator of a rational expression, with a variable in the argument of a logarithm, or a variable as the radicand in an nth root when n is an even number.
Often, in solving measurement equations, a negative answer shows up but measurements can't be negative.
the length of a rectangle is 2 more than its width
the area is 143
x*(x+2)=143
x^2+2x-143=0
(x-11)(x+13) =0
x=11
x=-13
-13 is extraneous
In cross multiplying you have to watch out for answers that would cause the denominator to be 0

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Cross-multiply:

or

Exclude because that makes the original RHS undefined.

John

My calculator said it, I believe it, that settles it

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