Help simplify...algebra?

Question

5x^2-18x-8 / 3x^2 - 48

([2x] / [x - 4] subtract (8) / (x^2 - 7x + 12) (fraction subtract fraction

([3x^2 + 10x - 8] / [x^2 -16]) / ([6x^2 - x - 2] / [x^2 -8x + 16]) (fraction divide fraction)

(2 + [5/x] + [3/x^2]) / (4 + [4/x] - [3/x^2]) (whole number plus fraction plus fraction divided by whole number plus fraction subtract fraction)

I hope this makes it easier to understand.

Answer 1

1.) (5X+2)/3(X+4)
2.) [(3X-2)(X-4)] / [2(3X+1)(X-1)]
3.) [(2X+3)(X+1)] / [(-X)(3X^3-4X-4)]

Answer 2

Simplifying fractions can get tedious, so use parentheses to keep things easy to manage. Basically we'll use two ideas, factoring of quadratic equations and common denominators.
1.)
( 5x^2 - 18x - 8 ) / ( 3x^2 - 48 )
(5x+2)(x-4) / 3(x-4)(x+4)
(5x+2) / 3(x+4)
SO
(5x+2) / (3x+12)

2.)
( 2x / x-4 ) - ( 8 / x^2 - 7x + 12 )
( 2x(x-3) / (x-4)(x-3) ) - ( 8 / (x-4)(x-3) )
2x^2-6x-8 / (x-4)(x-3)
2(x^2-3x-4) / (x-4)(x-3)
2(x-4)(x+1) / (x-4)(x-3)
2(x+1) / (x-3)
SO
(2x+2) / (x-3)

3.)
Multiply by reciprocal
(3x^2+10x-8) / (x^2-16) / (6x^2-x-2) / (x^2-8x+16)
(3x^2+10x-8)(x^2-8x+16) / (x^2-16)(6x^2-x-2)
(3x-2)(x+4)(x-4)(x-4) / (x+4)(x-4)(6x^2-x-2)
(3x-2)(x-4) / (6x^2-x-2)
SO
(3x^2-6x+8) / (6x^2-x-2)

4.)
Multiply by x^2 / x^2
2x^2+5x+3 / 4x^2+4x-3
Factor, SO
(2x+3)(x+1) / (4x^2+4x-3)

Hope this helps, look at some of these methods because they apply in most problems.

Answer 3

Just factor the top polynomial (5x^2-18x-8) then factor the bottom (3x^2 - 48) and see if they have any factors in common, which can be divided out. They have one factor in common. This is one polynomial divided by another.