Question 503562


{{{((3x^2-20x+25)/(2x^2-7x-15))/((6x^2-x-15)/(8x^2+18x+9))}}} Start with the given expression.



{{{((3x^2-20x+25)/(2x^2-7x-15))((8x^2+18x+9)/(6x^2-x-15))}}} Multiply the first fraction {{{(3x^2-20x+25)/(2x^2-7x-15)}}} by the reciprocal of the second fraction {{{(6x^2-x-15)/(8x^2+18x+9)}}}.



{{{(((3x-5)(x-5))/(2x^2-7x-15))((8x^2+18x+9)/(6x^2-x-15))}}} Factor {{{3x^2-20x+25}}} to get {{{(3x-5)(x-5)}}}.



{{{(((3x-5)(x-5))/((2x+3)(x-5)))((8x^2+18x+9)/(6x^2-x-15))}}} Factor {{{2x^2-7x-15}}} to get {{{(2x+3)(x-5)}}}.



{{{(((3x-5)(x-5))/((2x+3)(x-5)))(((2x+3)(4x+3))/(6x^2-x-15))}}} Factor {{{8x^2+18x+9}}} to get {{{(2x+3)(4x+3)}}}.



{{{(((3x-5)(x-5))/((2x+3)(x-5)))(((2x+3)(4x+3))/((2x+3)(3x-5)))}}} Factor {{{6x^2-x-15}}} to get {{{(2x+3)(3x-5)}}}.



{{{((3x-5)(x-5)(2x+3)(4x+3))/((2x+3)(x-5)(2x+3)(3x-5))}}} Combine the fractions. 



{{{(highlight((3x-5))highlight((x-5))highlight((2x+3))(4x+3))/(highlight((2x+3))highlight((x-5))(2x+3)highlight((3x-5)))}}} Highlight the common terms. 



{{{(cross((3x-5))cross((x-5))cross((2x+3))(4x+3))/(cross((2x+3))cross((x-5))(2x+3)cross((3x-5)))}}} Cancel out the common terms. 



{{{(4x+3)/(2x+3)}}} Simplify. 



So {{{((3x^2-20x+25)/(2x^2-7x-15))/((6x^2-x-15)/(8x^2+18x+9))}}} simplifies to {{{(4x+3)/(2x+3)}}}.



In other words, {{{((3x^2-20x+25)/(2x^2-7x-15))/((6x^2-x-15)/(8x^2+18x+9))=(4x+3)/(2x+3)}}}



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Jim