Question

Answer 1

a: \(\dfrac{4x^2}{10x^2y}=\dfrac{4x^2:2x^2}{10x^2y:2x^2}=\dfrac{2}{5y}\)

b: \(\dfrac{5x+10}{25x^2+50x}=\dfrac{5\cdot x+5\cdot2}{5x\cdot5x+5x\cdot10}\)

\(=\dfrac{5x+10}{5x\left(5x+10\right)}=\dfrac{1}{5x}\)

c: \(\dfrac{6x^2y^2}{8xy^3}=\dfrac{2xy\cdot3xy}{2xy\cdot4y^2}=\dfrac{3xy}{4y^2}\)

d: \(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}=\dfrac{5xy\left(x+y\right)\cdot2y}{5xy\left(x+y\right)\cdot3\left(x+y\right)^2}=\dfrac{2y}{3\left(x+y\right)^2}\)

e: \(\dfrac{2x^2+2x}{x+1}=\dfrac{2x\cdot x+2x\cdot1}{x+1}=\dfrac{2x\left(x+1\right)}{x+1}=2x\)