`@Akira`
`a)\frac{x^2+7x+12}{4x^2+12x}`
`=\frac{x^2+3x+4x+12}{4x.(x+3)}`
`=\frac{x(x+3)+4(x+3)}{4x(x+3)}`
`=\frac{(x+3)(x+4)}{4x(x+3)}`
`=\frac{x+4}{4x}`
`b)\frac{5x^3-20x}{x^3-x-2}`
`=\frac{5x(x^2-4)}{x^2+x-2x-2}`
`=\frac{5x(x-2)(x+2)}{x(x+1)-2(x+1)}`
`=\frac{5x(x-2)(x+2)}{(x+1)(x-2)}`
`=\frac{5x(x+2)}{x+1}`
`=\frac{5x^2+10x}{x+1}`
`c)\frac{x^2-8x+12}{x^2-2x-24}`
`=\frac{x^2-2x-6x+12}{x^2+4x-6x-24}`
`=\frac{x(x-2)-6(x-2)}{x(x+4)-6(x+4)}`
`=\frac{(x-2)(x-6)}{(x+4)(x-6)}`
`=\frac{x-2}{x+4}`
`d)\frac{4x^2-12x+9}{2x^2-13+15}`
`=\frac{(2x)^2-2.2x.3+(3)^2}{2x^2-3x-10x+15}`
`=\frac{(2x-3)^2}{x(2x-3)-5(2x-3)}`
`=\frac{(2x-3)^2}{(2x-3)(x-5)}`
`=\frac{2x-3}{x-5}`
