Question

Please help me I am having a hard time with this activity

Answer 1

Explanation:

b.

`(a^2+6a+9)/(a^2-9) *(3a-9)/(a+3) \\=(a^2+2*a*3+3^2)/(a^2-3^2) *(3(a-3))/(a+3) \\=((a+3)^2)/((a+3)(a-3)) *(3(a-3))/(a+3) \\=(3(a+3)^2)/((a+3)^2) \\=3`

d.

`(3x^2-6x)/(3x+1) *(x+3x^2)/(x^2-4x+4) \\=(3x(x-2))/(3x+1) *(x(1+3x))/(x^2-2x-2x+4) \\=(3x(x-2))/(3x+1) *(x(1+3x))/(x(x-2)-2(x-2)) \\=(3x(x-2))/(3x+1) *(x(1+3x))/((x-2)(x-2) ) \\=(3x^2)/(x-2))`

e.

`(2x^2-10x+12)/(x^2-4) *(2+x)/(3-x) \\=(2[x^2-5x+6])/(x^2-2^2) *(2+x)/(-(-3+x)) \\=(2[x^2-2x-3x+6])/((x+2)(x-2)) *(x+2)/(-(x-3)) \\=(2[x(x-2)-3(x-2)])/((x+2)(x-2)) *(x+2)/(-(x-3)) \\=(2(x-2)(x-3))/((x+2)(x-2)) *(x+2)/(-(x-3)) \\=(2)/(-1) \\=-2`

k.

`(6x^2-11x-10)/(6x^2-5x-6) *(6-4x)/(25-20x+4x^2) \\=(6x^2-15x+4x-10)/(6x^2-9x+4x-6) *(-4x+6)/(4x^2-10x-10x+25) \\=(3x(2x-5)+2(2x-5))/(3x(2x-3)+2(2x-3) ) *(-2(2x-3))/(2x(2x-5)-5(2x-5)) \\=((2x-5)(3x+2))/((2x-3)(3x+2)) *(-2(2x-3))/((2x-5)(2x-5)) \\=(-2)/(2x-5)`