Question

Answer 1

a)
\(\dfrac{6x^2+9x}{4x^2-9}=\dfrac{3x}{A}\Rightarrow A=3x.\dfrac{4x^2-9}{6x^2+9x}\Rightarrow A=3x.\dfrac{\left(2x\right)^2-3^2}{3x\left(2x+3\right)}\Rightarrow A=\dfrac{\left(2x-3\right)\left(2x+3\right)}{2x+3}\Rightarrow A=2x-3\)

b)

\(\dfrac{5\left(x+y\right)}{3}=\dfrac{5x^2-5y^2}{A}\Rightarrow A=5x^2-5y^2.\dfrac{3}{5\left(x+y\right)}\Rightarrow A=5\left(x^2-y^2\right).\dfrac{3}{5\left(x+y\right)}\Rightarrow A=\dfrac{3\left(x^2-y^2\right)}{x+y}\Rightarrow A=\dfrac{3\left(x-y\right)\left(x+y\right)}{x+y}\Rightarrow A=3\left(x-y\right)\)