Question 113020
{{{((2x^2 + 5x - 12)/ (9x^2 - 16)) /((2x^2 - 7x + 6)/ (3x^2 - x - 4)) }}} Start with the given expression



{{{((2x^2 + 5x - 12)/ (9x^2 - 16)) *((3x^2-x-4)/(2x^2-7x+6))}}} Multiply the first fraction by the reciprocal of the second fraction



{{{(((x+4)(2x-3))/(9x^2-16))*((3x^2-x-4)/(2x^2-7x+6))}}} Factor {{{2x^2+5x-12}}} to get {{{(x+4)(2x-3)}}}  (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)


{{{(((x+4)(2x-3))/((3x-4)(3x+4)))*((3x^2-x-4)/(2x^2-7x+6))}}} Factor {{{9x^2-16}}} to get {{{(3x-4)(3x+4)}}}  


{{{(((x+4)(2x-3))/((3x-4)(3x+4)))*(((3x-4)(x+1))/(2x^2-7x+6))}}} Factor {{{3x^2-x-4}}} to get {{{(3x-4)(x+1)}}}  


{{{(((x+4)(2x-3))/((3x-4)(3x+4)))*(((3x-4)(x+1))/((x-2)(2x-3)))}}} Factor {{{2x^2-7x+6}}} to get {{{(x-2)(2x-3)}}}




{{{(((x+4)cross((2x-3)))/(cross((3x-4))(3x+4)))*((cross((3x-4))(x+1))/((x-2)cross((2x-3))))}}} Cancel like terms



{{{(((x+4))/((3x+4)))*(((x+1))/((x-2)))}}} Simplify 



{{{((x+4)(x+1))/((3x+4)(x-2))}}} Combine the fractions



So {{{((2x^2 + 5x - 12)/ (9x^2 - 16)) /((2x^2 - 7x + 6)/ (3x^2 - x - 4)) }}} simplifies to {{{((x+4)(x+1))/((3x+4)(x-2))}}}