i need help
(t² - t - 6)/(t² + 2t - 15) × (t + 5)/(t² - 4t - 5)
= (t - 3)(t + 2)(t + 5) / (t + 5)(t - 3)((t - 5)(t + 1)
= (t + 2) / (t - 5)(t + 1)
( t - 3 ) ( t + 2 ) ( t + 5 )
-----------------------------------------
( t + 5 ) ( t - 3 ) ( t - 5 )( t + 1 )
t + 2
-------------------
( t - 5 ) ( t + 1 )
Short method:
Factorize both numerator and denominators and simplify
( t² - t - 6 ) / ( t² + 2t -15 )
= [ ( t + 2 ) ( t - 3 ) ] / [ ( t + 5 ) ( t - 3 ) ]
= ( t + 2 ) / ( t + 5 )
Long method:
let’s express the numerator in another way= ( t² + 2t -15 - 3t + 9 ) / ( t² + 2t -15 )
= ( t² + 2t -15 ) / ( t² + 2t -15 ) - ( 3t - 9 ) / ( t² + 2t -15 )
= 1 - 3( t - 3 ) / ( t² + 2t -15 )
= 1 - 3( t - 3 ) / [ ( t + 5 ) ( t - 3 ) ]
= 1 - 3/( t + 5 )
= ( t + 5 - 3 ) / ( t + 5 )
Factor then cancel:
(t - 3)(t + 2) (t + 5)
-------------- • -----------
(t + 5)(t - 3) (t - 5)(t+1)
After canceling all that's left is (t + 2) over (t - 5)(t + 1)
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Verified answer
(t² - t - 6)/(t² + 2t - 15) × (t + 5)/(t² - 4t - 5)
= (t - 3)(t + 2)(t + 5) / (t + 5)(t - 3)((t - 5)(t + 1)
= (t + 2) / (t - 5)(t + 1)
( t - 3 ) ( t + 2 ) ( t + 5 )
-----------------------------------------
( t + 5 ) ( t - 3 ) ( t - 5 )( t + 1 )
t + 2
-------------------
( t - 5 ) ( t + 1 )
Short method:
Factorize both numerator and denominators and simplify
( t² - t - 6 ) / ( t² + 2t -15 )
= [ ( t + 2 ) ( t - 3 ) ] / [ ( t + 5 ) ( t - 3 ) ]
= ( t + 2 ) / ( t + 5 )
Long method:
( t² - t - 6 ) / ( t² + 2t -15 )
let’s express the numerator in another way= ( t² + 2t -15 - 3t + 9 ) / ( t² + 2t -15 )
= ( t² + 2t -15 ) / ( t² + 2t -15 ) - ( 3t - 9 ) / ( t² + 2t -15 )
= 1 - 3( t - 3 ) / ( t² + 2t -15 )
= 1 - 3( t - 3 ) / [ ( t + 5 ) ( t - 3 ) ]
= 1 - 3/( t + 5 )
= ( t + 5 - 3 ) / ( t + 5 )
= ( t + 2 ) / ( t + 5 )
Factor then cancel:
(t - 3)(t + 2) (t + 5)
-------------- • -----------
(t + 5)(t - 3) (t - 5)(t+1)
After canceling all that's left is (t + 2) over (t - 5)(t + 1)