Question

multiply or divide and then simplify

(x+1)^2/(x-5)*(x-3)/(x+1)

3x+3/2 divided by 4/9x+9

4a/3a-3*3(a-1)/16a

x+2/x-1 divided by 5x+10/x-2

Answer 1

`((x+1)^2)/(x-5)\cdot(x-3)/(x+1)=(x+1)/(x-5)\cdot(x-3)/(1)=((x+1)(x-3))/(x-5)=(x^2-3x+x-3)/(x-5)=(x^2-2x-3)/(x-5)\\\\D:x\\eq5\ \wedge\ x\\eq-1`



`(3x+3)/(2):(4)/(9x+9)=(3x+3)/(2)\cdot(9x+9)/(4)=(27x^2+27x+27x+27)/(8)=(27x^2+54x+27)/(8)\\\\D:x\\eq1`



`(4a)/(3a-3)\cdot(3(a-1))/(16a)=(1)/(3a-3)\cdot(3a-3)/(4a)=(1)/(4a)\\\\D:a\\eq1\ \wedge\ a\\eq0`



`(x+2)/(x-1):(5x+10)/(x-2)=(x+2)/(x-1)\cdot(x-2)/(5x+10)=(x+2)/(x-1)\cdot(x-2)/(5(x+2))=(1)/(x-1)\cdot(x-2)/(5)=(x-2)/(5x-5)\\\\D:x\\eq1\ \wedge\ x\\eq2\ \wedge\ x\\eq-2`