SOLUTION: Could you please help with these? I have tried to work them, but I keep getting confused. simplify the rational expression x^2 - 3x - 10 ___________ ____ x^2 - x - 20

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Could you please help with these? I have tried to work them, but I keep getting confused. simplify the rational expression x^2 - 3x - 10 ___________ ____ x^2 - x - 20       Log On


   

Question 33473: Could you please help with these? I have tried to work them, but I keep getting confused.
simplify the rational expression
x^2 - 3x - 10
________________
x^2 - x - 20


Divide
2x^2 + 5x - 12 2x^2 - 7x + 6
__________________ / ________________
9x^2 - 16 3x^2-x-4


Rationalize the denominator:

__________2__________
sqrt [6]- sqrt [5]
Answer by sarah_adam(201) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-3x-10%29%2F%28x%5E2-x-20%29
%28x%5E2-3x-10%29 = %28x%5E2-5x%2B2x-10%29
x(x-5)+2(x-5)
(x+2)(x-5)
%28x%5E2-x-20%29 = %28x%5E2-5x%2B4x-20%29
x(x-5)+4(x-5)
(x+4)(x-5)
now %28x%2B2%29%28x-5%29%2F%28x%2B4%29%28x-5%29
%28x%2B2%29%2F%28x%2B4%29
---------------------------------------------------------------------
2x^2 + 5x - 12 2x^2 - 7x + 6
__________________ / ________________
9x^2 - 16 3x^2-x-4
Now taking the numerator and denominator separately and factorizing seperately
2x^2 + 5x - 12
__________________
9x^2 - 16


2x^2+8x-3x-12
-------------
(3x)^2 - (4)^2


2x(x+4)-3(x+4)
--------------
(3x-4)(3x+4)


(2x-3)(x+4)
------------
(3x-4)(3x+4)


Now the denominator

2x^2 - 7x + 6
__________________
3x^2-x-4


2x^2-4x-3x+6
-------------
(3x)^2 -4x+3x-4


2x(x-2)-3(x-2)
--------------
x(3x-4)+1(3x-4)


(2x-3)(x+4)
------------
(x+1)(3x-4)


Numerator / Denominator


(2x-3)(x+4)
------------
(3x-4)(3x+4)
__________________
(2x-3)(x+4)
------------
(x+1)(3x-4)


(2x-3)(x+4) (x+1)(3x-4)
------------ * ------------
(3x-4)(3x+4) (2x-3)(x+4)


cancelling the common terms and simplifying we get
(x+1)
-----
(3x+4)
_______________________________________________________________

Rationalize the denominator
2%2F%28sqrt%286%29+-+sqrt%285%29%29
multiply the numerator and denominator with %28sqrt%286%29+%2B+sqrt%285%29%29
2%2A%28sqrt%286%29+%2Bsqrt%285%29%29/(6 - 5)
2%2A%28sqrt%286%29+%2Bsqrt%285%29%29