I have to solve the following equation.
I suspect the LCD (lowest common denominator) is and some factor of But I couldn't factor this last expression.
According to the book answers the solution is -6
Wow...wait. How did you do that? I mean the formulae for the perfect square trinomials are
or
Which is the same as:
or
And then I thought of as being equivalent
to and therefore:
should have been equal to but this didn't fit into my solution.
After that I noticed that according to the formulae, in a perfect square, the last term, b, should alway be positive while mine, -4, is negative. How did you know it is a perfect square trinomial when it doesn't match these formulae and how did you factor it??
Just hope there are not too many questions...It is only that an answer now will solve many questions in the future.
I'm not sure why you thought that is a perfect square trinomial. As an example, is a perfect square trinomial because
(1) is a perfect square,
(2) The constant term, 4 is perfect square (and it must be positive), and
(3) the middle term, 4y, is twice the product of y and 2, the square roots of the two outer terms. (This can be negative.)
So .
Since is not a perfect square trinomial, you have to find the factors by guess-and-check.
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