Question

Simplify the expression:

3x (4x-6)
—————
2x(3x)

Answer 1

`=(2x-3)/(x)`

Explanation:

`=6x^2\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=(3x\left(4x-6\right))/(2x\cdot \:3x)\\2x\cdot \:3x=6x^2\\=(3x\left(4x-6\right))/(6x^2)\\\mathrm{Cancel\:}(3x\left(4x-6\right))/(6x^2):\quad (4x-6)/(2x)\\=(4x-6)/(2x)\\\mathrm{Factor}\:4x-6:\quad 2\left(2x-3\right)\\=(2\left(2x-3\right))/(2x)\\\mathrm{Divide\:the\:numbers:}\:(2)/(2)=1\\=(2x-3)/(x)`