Question

How to simplify the fractions

Answer 1

`\large\boxed{(3x+6)/(x-4)/(2x^2+9x+10)/(x^2+4x)=(3x(x+4))/((x-4)(2x+5))}`

Explanation:

Just like that

`(3x+6)/(x-4)/(2x^2+9x+10)/(x^2+4x)=(3x+6)/(x-4)\cdot(x^2+4x)/(2x^2+9x+10)\\\\=(3(x+2))/((x-4))\cdot(x(x+4))/(2x^2+4x+5x+10)=(3(x+2))/((x-4))\cdot(x(x+4))/(2x(x+2)+5(x+2))\\\\=(3(x+2))/((x-4))\cdot(x(x+4))/((x+2)(2x+5))\qquad\text{cancel}\ (x+2)\\\\=(3x(x+4))/((x-4)(2x+5))`