Question

Answer 1

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

b) \(\dfrac{x\left(x^2-4\right)}{x+2}=\dfrac{x\left(x-2\right)\left(x+2\right)}{x+2}=x\left(x-2\right)\)

c) \(\dfrac{x^2+2x}{2x+4}=\dfrac{x\left(x+2\right)}{2\left(x+2\right)}=\dfrac{x}{2}\)

d) \(\dfrac{m^2-4m+4}{2m-4}=\dfrac{\left(m-2\right)^2}{2\left(m-2\right)}=\dfrac{m-2}{2}\)

Answer 2

\(\dfrac{x^2+2x}{4-x^2}=\dfrac{x.\left(x+2\right)}{\left(2-x\right).\left(2+x\right)}=\dfrac{x}{2-x}\\ \dfrac{x.\left(x^2-4\right)}{x+2}=\dfrac{x.\left(x-2\right).\left(x+2\right)}{x+2}=x.\left(x-2\right)\\ \dfrac{x^2+2x}{2x+4}=\dfrac{x.\left(x+2\right)}{2.\left(x+2\right)}=\dfrac{x}{2}\\ \dfrac{m^2-4m+4}{2m-4}=\dfrac{\left(m-2\right)^2}{2.\left(m-2\right)}=\dfrac{m-2}{2}\)