Question

Answer 1

a: \(\frac{x^2-y^2}{6x^2y}:\frac{x+y}{3xy}\)

\(=\frac{\left(x-y\right)\left(x+y\right)}{6x^2y}\cdot\frac{3xy}{x+y}=\frac{\left(x-y\right)}{2x}\)

b: \(\frac{25x^3y^3}{3}:15xy^2\)

\(=\frac{25x^3y^3}{3\cdot15xy^2}=\frac{25}{45}\cdot\frac{x^3}{x}\cdot\frac{y^3}{y^2}=\frac59x^2y\)

c: \(\frac{x+y}{y-x}:\frac{x^2+xy}{3x^2-3y^2}\)

\(=\frac{-\left(x+y\right)}{x-y}\cdot\frac{3\left(x-y\right)\left(x+y\right)}{x\left(x+y\right)}=\frac{-3\left(x+y\right)}{x}\)

d: \(\frac{x^2-9y^2}{x^2y^2}\cdot\frac{3xy}{2x-6y}\)

\(=\frac{\left(x-3y\right)\left(x+3y\right)}{x^2y^2}\cdot\frac{3xy}{2\left(x-3y\right)}=\frac{x+3y}{xy}\cdot\frac32=\frac{3x+9y}{2xy}\)

e: \(\frac{x^2-36}{2x+12}\cdot\frac{4}{6-x}\)

\(=-\frac{4\left(x-6\right)\left(x+6\right)}{2\left(x+6\right)\left(x-6\right)}=-\frac42=-2\)