19 011 points SAIgTrig4 07023 Simplify the rational expressi

19. (0-11 points SAIgTrig4 0.7.023 Simplify the rational expression. 5x3-13x2-6x 5x2 17x 6 Need Help? Watch Submit Answer Save Progress 20. 0-11 points SAIgTrig4 0.7.033 Perform the multiplication or division and simplify. x+3x2 6x 9 25x2 16 5x26x - 8 Need Help? Watch t 21. 1/1 points | Previous Answers SAlgTrig4 0.7.049 Perform the addition or subtraction and simplify. 9 x2 x2+3x 10x +3

Solution

1) ( 5x^3 -13x^2 - 6x ) / ( 5x^2 - 17x + 6)

factoring the top and bottom part

5x^3 -13x^2 - 6x = x ( x - 3) ( 5x + 2)

5x^2 - 17x + 6 = ( x- 3) ( 5x - 2)

so we can write

x ( x - 3) ( 5x + 2) /  ( x- 3) ( 5x - 2)

simplified form is

x ( 5x + 2) / ( 5x - 2)

2) ( x+3) / ( 25x^2 - 16 ) / (x^2 + 6x + 9 ) / ( 5x^2 + 6x - 8 )

factoring each expression

( x+ 3) / ( 5x - 4) ( 5x + 4) * ( x+ 2) ( 5x - 4) / ( x+3) (x+3)

simplifying we get

( x+ 2) / ( 5x + 4) ( x + 3)