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If boths sides of an equation are divided by a factor that includes a variable, a number of steps should be taken to be sure a root of the given equation is not removed. Which of the following is NOT one of those steps?

A.Check all root values in the given equation

B.Factor or use the quadratic equation if applicable

C.Set the factor equal to zero and solve for the variable

D.Square one side of the remaining equation

Mar 8, 2018

#1
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If it is difficult for you to comprehend this problem, then it may be best to think of an example. Don't overcomplicate matters, though! I think $$\frac{x^3+5x^2}{x}=0$$ is an adequate example because this equation involved the elimination of a variable.

If you were to solve it, it may look something like this!

$$\frac{x^3+5x^2}{x}=0\\ \frac{x^2(x+5)}{x}=0\\ x(x+5)=0\\ x=0\text{ and }x=-5$$

A) Confirming the validity of all roots is essential. Notice that $$x=0$$ in the previous example is an extraneous solution because it results in a division-by-zero error.

B) Factoring was essential to recognize that there was a common factor in the first place!

C) Yes, this is a necessary precaution. If we set the common factor equal to zero, then we will get that $$x\neq0$$ because this does not fit the domain.

D) This step is illogical; do not do this.

Mar 8, 2018
#2
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Thank You!!!

Mar 8, 2018