Question 1160804
  Reduce the following rational expressions to their simplest form.
A)


{{{(5x-10)/5x}}}


{{{5(x-2)/5x}}}


{{{cross(5)(x-2)/cross(5)x}}}


{{{(x-2)/x}}}



B) 


{{{(8x+56)/(4x-28)}}}


{{{8(x+7)/4(x-7)}}}


{{{cross(8)2(x+7)/cross(4)(x-7)}}}


{{{2(x+7)/(x-7)}}}



C)


 {{{(15x^2+9x^3)/(15x^2+9x)}}}


{{{3x^2(5+3x)/3x(5x+3)}}}


{{{cross(3x^2)x(5+3x)/cross(3x)(5x+3)}}}


{{{x(5+3x)/(5x+3)}}}



D) 


{{{(6x-3)/(1-2x)}}}


{{{(-3+6x)/(1-2x)}}}


{{{-3(1-2x)/(1-2x)}}}


{{{-3cross((1-2x))/cross((1-2x))}}}


{{{-3}}}



E) 


{{{(3x^2-48)/(24-6x)}}}


{{{(3(x^2-16))/(6(4-x))}}}


{{{(cross(3)(x^2-4^2))/(-cross(6)2(x-4))}}}


{{{((x-4)(x+4))/(-2(x-4))}}}


{{{(cross((x-4))(x+4))/(-2cross((x-4)))}}}


{{{(x+4)/(-2)}}}


{{{-(x+4)/2}}}



7. Simplifying the following by adding and subtracting.


A) 


{{{(x+2)/12-(5-3x)/3-(5x)/2}}}....common denominator is {{{12}}}


{{{(x+2)/12-4(5-3x)/12-6(5x)/12}}}


{{{(x+2)/12-(20-12x)/12-(30x)/12}}}


{{{(x+2-(20-12x)-30x)/12}}}


{{{(x+2-20+12x-30x)/12}}}


{{{(-17x - 18)/12}}}



B)

{{{ (x+2)/(5x^2)-(3-4x)/6}}}.......common denominator {{{30x^2}}}


{{{ 6(x+2)/(30x^2)-(5x^2(3-4x))/(30x^2)}}}


{{{ (6(x+2)-(5x^2(3-4x)))/(30x^2)}}}


{{{ (6x+12-(15x^2-20x^3))/(30x^2)}}}


{{{ (20x^3 - 15x^2 + 6x + 12)/(30x^2)}}}

{{{ 20x^3/(30x^2) - 15x^2/(30x^2) + 6x/(30x^2) + 12/(30x^2)}}}

{{{ 2x/3 - 1/2 + 1/(5x) + 2/(5x^2)}}}


C)


{{{ 5x/(4x-3)-3x/(2x+3)}}}


{{{ (5x(2x+3))/((4x-3)(2x+3))-(3x(4x-3))/((2x+3)(4x-3))}}}


{{{ (10x^2+15x-(12x^2-9x))/((2x+3)(4x-3))}}}


{{{ (10x^2+15x-12x^2+9x)/((2x+3)(4x-3))}}}


{{{ (-2x^2+24x)/((2x+3)(4x-3))}}}


{{{ -2x(x-12)/((2x+3)(4x-3))}}}



d) 


{{{(x+2)/(49-x^2)-4/(3x-21)}}}


{{{(x+2)/(-(x^2-7^2))-4/3(x-7)}}}


{{{-(x+2)/((x-7)(x+7))-4/3(x-7)}}}


{{{-3(x+2)/(3(x-7)(x+7))-(4(x+7))/(3(x-7)(x+7))}}}


{{{(-3(x+2)-4(x+7))/(3(x-7)(x+7))}}}


{{{(-7x - 34)/(3(x-7)(x+7))}}}