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

$\frac{(x+1)^2}{x-5}\cdot\frac{x-3}{x+1}=\frac{x+1}{x-5}\cdot\frac{x-3}{1}=\frac{(x+1)(x-3)}{x-5}=\frac{x^2-3x+x-3}{x-5}=\frac{x^2-2x-3}{x-5}\\\\D:x\neq5\ \wedge\ x\neq-1$


$\frac{3x+3}{2}:\frac{4}{9x+9}=\frac{3x+3}{2}\cdot\frac{9x+9}{4}=\frac{27x^2+27x+27x+27}{8}=\frac{27x^2+54x+27}{8}\\\\D:x\neq1$


$\frac{4a}{3a-3}\cdot\frac{3(a-1)}{16a}=\frac{1}{3a-3}\cdot\frac{3a-3}{4a}=\frac{1}{4a}\\\\D:a\neq1\ \wedge\ a\neq0$


$\frac{x+2}{x-1}:\frac{5x+10}{x-2}=\frac{x+2}{x-1}\cdot\frac{x-2}{5x+10}=\frac{x+2}{x-1}\cdot\frac{x-2}{5(x+2)}=\frac{1}{x-1}\cdot\frac{x-2}{5}=\frac{x-2}{5x-5}\\\\D:x\neq1\ \wedge\ x\neq2\ \wedge\ x\neq-2$