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.Com
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) (Show Source): You can put this solution on YOUR website!
=
x(x-5)+2(x-5)
(x+2)(x-5)
=
x(x-5)+4(x-5)
(x+4)(x-5)
now
---------------------------------------------------------------------
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
multiply the numerator and denominator with
/(6 - 5)
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