Question

Answer 1

a: \(\dfrac{4}{x^2-4y^2}=\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}=\dfrac{8x}{2x\left(x-2y\right)\left(x+2y\right)}\)

\(\dfrac{5}{2x^3-8xy^2}=\dfrac{5}{2x\left(x^2-4y^2\right)}=\dfrac{5}{2x\left(x-2y\right)\left(x+2y\right)}\)

b: \(\dfrac{2}{2x^2-6x}=\dfrac{2}{2x\left(x-3\right)}=\dfrac{1}{x\left(x-3\right)}=\dfrac{x-5}{x\left(x-3\right)\left(x-5\right)}\)

\(\dfrac{6}{x^2-8x+15}=\dfrac{6x}{x\left(x-3\right)\left(x-5\right)}\)

c: \(\dfrac{2-x}{3xy}=\dfrac{\left(2-x\right)\cdot10\cdot x^3y^2}{30x^4y^3}\)

\(\dfrac{3}{5xy^3}=\dfrac{18x^3}{30x^4y^3}\)

\(\dfrac{1-y}{10x^4}=\dfrac{\left(1-y\right)\cdot3y^3}{30x^4y^3}\)