Only final factored variable hold relevance? & extraneous solutions..

[bobisaka]

Probably a stupid question but..in the highlighted step below, what happens to the factored 3?
Does the factored 3 become irrelevant, because we are able to get the y by itself in its final factor?

Why is y=-6 an extraneous solution?

 

[Deleted member 4993]

Probably a stupid question but..in the highlighted step below, what happens to the factored 3?
Does the factored 3 become irrelevant, because we are able to get the y by itself in its final factor?

Why is y=-6 an extraneous solution?

View attachment 18922

Check y = -6 in the original equation.

The denominators become zero and ..... everything blows-up.

Thus y = -6 is an extraneous (meaning that solution is false).

 

[lev888]

Probably a stupid question but..in the highlighted step below, what happens to the factored 3?
Does the factored 3 become irrelevant, because we are able to get the y by itself in its final factor?

We divide both sides by 3. 0/3 = 0, so we still have 0 on the left.

 

[Dr.Peterson]

Probably a stupid question but..in the highlighted step below, what happens to the factored 3?
Does the factored 3 become irrelevant, because we are able to get the y by itself in its final factor?

Another way to think about the 3 is that 3(y+6)(y-4) can be zero only if one of its factors is zero. The factors are 3, (y+6), and (y-4).

• Since 3 can't be zero, we can ignore it!
• If y+6 is zero, we get y = -6, which is not in the domain of the equation.
• If y-4 is zero, we get y = 4, which works.