Question

BT: Quy đồng các mẫu thức sau a) 1/2x-3 ; 2x-3/2x ²-18 ; 4/2x ²+3x-9

Answer 1

\(\dfrac{1}{2x-3}=\dfrac{2\left(x-3\right)\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)\left(2x-3\right)}\)

\(\dfrac{2x-3}{2x^2-18}=\dfrac{2x-3}{2\left(x-3\right)\left(x+3\right)}=\dfrac{\left(2x-3\right)\cdot\left(2x-3\right)}{2\left(2x-3\right)\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{\left(2x-3\right)^2}{2\left(2x-3\right)\left(x-3\right)\left(x+3\right)}\)

\(\dfrac{2}{2x^2+3x-9}=\dfrac{2}{\left(x+3\right)\left(2x-3\right)}=\dfrac{2\cdot2\cdot\left(x-3\right)}{2\left(x-3\right)\cdot\left(x+3\right)\left(2x-3\right)}\)

\(=\dfrac{4x-12}{2\left(x-3\right)\left(x+3\right)\left(2x-3\right)}\)