What is wrong with the following equation? x^2+x-6/x-2=x+3

Dillard

Dillard

Answered question

2021-09-23

What is wrong with the following equation?
x2+x6x2=x+3

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-09-24Added 97 answers

Factor the left side
x2+x6x2=(x2)(x+3)x2
Then cancel out the common factor
x2+x6x2=(x2)(x+3)x2=x+3
However, note that while plugging x=2 into the expression x+3 seems to be ok, doing the same for the original expression x2+x6x2 is not because you would have a 0 denominator.
So you can not say that x+3 is equal to x2+x6x2 unless you say
x2+x6x2=x+3,x2
that is, you must explicitly exclude numbers not in the domain of the original
Result: you must also state that x2
xleb123

xleb123

Skilled2023-05-26Added 181 answers

Result:
all real numbers x
Solution:
(x2+x6)=(x+3)(x2)
Next, we can expand the right side of the equation using the distributive property:
x2+x6=x2+x6
We can observe that both sides of the equation are identical. This means that the equation is an identity, and it is true for all values of x. Therefore, the given equation does not have a specific solution; instead, it holds true for any value of x.
Hence, the solution to the equation x2+x6x2=x+3 is all real numbers x.

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