SOLUTION: Simplify the expression. (9 - tanēθ) / (tanēθ - 5tanθ + 6)

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Question 985660: Simplify the expression.
(9 - tanēθ) / (tanēθ - 5tanθ + 6)
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
%289+-+tan%5E2%28theta%29%29+%2F+%28tan%5E2%28theta%29+-+5tan%28theta%5E%22%22%29+%2B+6%29

Let u+=+tan%28theta%29

%289+-+u%5E2%29+%2F+%28u%5E2+-+5u+%2B+6%29

Get numerator in descending order:
Factor denominator

%28-u%5E2%2B9%29+%2F+%28%28u-3%29%28u-2%29%29

Factor -1 out of numerator:

%28-%28u%5E2-9%29%29+%2F+%28%28u-3%29%28u-2%29%29

Complete factoring of numerator:

%28-%28%28u-3%29%5E%22%22%28u%2B3%29%29%29+%2F+%28%28u-3%29%5E%22%22%28u-2%29%29

%28-%28cross%28%28u-3%29%29%28u%2B3%29%29%29+%2F+%28cross%28%28u-3%29%29%28u-2%29%29

-%28u%2B3%29+%2F+%28u-2%29

Substitute u+=+tan%28theta%29

-%28tan%28theta%29%2B3%29+%2F+%28tan%28theta%29-2%29

Edwin