Question

What is the product? 2y/y-13 * 4y-12/2y+6

Answer 1

12/6

Explanation:

Answer 2

`=(4y)/(y+3)`

Explanation:

`(2y)/(y-3)\cdot (4y-12)/(2y+6)\\(4y-12)/(2y+6)=(2\left(y-3\right))/(y+3)\\(4y-12)/(2y+6)\\\mathrm{Factor}\:4y-12:\quad 4\left(y-3\right)\\4y-12\\\mathrm{Rewrite\:as}\\=4y-4\cdot \:3\\\mathrm{Factor\:out\:common\:term\:}4\\=4\left(y-3\right)\\=(4\left(y-3\right))/(2y+6)\\\mathrm{Factor}\:2y+6:\quad 2\left(y+3\right)\\2y+6\\\mathrm{Rewrite\:as}\\=2y+2\cdot \:3\\\mathrm{Factor\:out\:common\:term\:}2\\=2\left(y+3\right)\\=(4\left(y-3\right))/(2\left(y+3\right))`

`\mathrm{Divide\:the\:numbers:}\:(4)/(2)=2\\=(2\left(y-3\right))/(\left(y+3\right))\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=(2\left(y-3\right))/(y+3)\\=(2y)/(y-3)\cdot (2\left(y-3\right))/(y+3)\\\mathrm{Multiply\:fractions}:\quad (a)/(b)\cdot (c)/(d)=(a\:\cdot \:c)/(b\:\cdot \:d)\\=(2y\cdot \:2\left(y-3\right))/(\left(y-3\right)\left(y+3\right))\\\mathrm{Cancel\:the\:common\:factor:}\:y-3\\=(2y\cdot \:2)/(y+3)`

`\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4\\=(4y)/(y+3)`