What is (9-tan^2(θ))/(tan^2(θ)-5tan(θ)+6) ?

The solution to (9-tan^2(θ))/(tan^2(θ)-5tan(θ)+6) is -(tan(θ)+3)/(tan(θ)-2)

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simplify (9-tan^2(θ))/(tan^2(θ)-5tan(θ)+6)

simplify

\frac{9 - tan ^{2} ( θ )}{tan ^{2} ( θ ) - 5 tan ( θ ) + 6}

- \frac{tan ( θ ) + 3}{tan ( θ ) - 2}

Solution steps

\frac{9 - tan ^{2} ( θ )}{tan ^{2} ( θ ) - 5 tan ( θ ) + 6}

Factor

9 - tan^{2} (θ) : - (tan (θ) + 3) (tan (θ) - 3)

= - \frac{( tan ( θ ) + 3 ) ( tan ( θ ) - 3 )}{tan ^{2} ( θ ) - 5 tan ( θ ) + 6}

Factor

tan^{2} (θ) - 5 tan (θ) + 6 : (tan (θ) - 2) (tan (θ) - 3)

= - \frac{( tan ( θ ) + 3 ) ( tan ( θ ) - 3 )}{( tan ( θ ) - 2 ) ( tan ( θ ) - 3 )}

Cancel the common factor:

tan (θ) - 3

= - \frac{tan ( θ ) + 3}{tan ( θ ) - 2}

1 6^{2} - x

\frac{( a + b ) ^{3} - ( c + d ) ^{3}}{( a + b ) - ( c + d )}

2 f (x)

(7 a + 10 b + 2 c) - (3 a - c)

(1 + 1)

What is (9-tan^2(θ))/(tan^2(θ)-5tan(θ)+6) ?
The solution to (9-tan^2(θ))/(tan^2(θ)-5tan(θ)+6) is -(tan(θ)+3)/(tan(θ)-2)