Question

Answer 1

a: \(\dfrac{x^2-3x+1}{4x^2}+\dfrac{5x-1-x^2}{4x^2}\)

\(=\dfrac{x^2-3x+1+5x-1-x^2}{4x^2}=\dfrac{2x}{4x^2}=\dfrac{1}{2x}\)

b: \(\dfrac{y}{x-y}+\dfrac{x}{x+y}\)

\(=\dfrac{y\left(x+y\right)+x\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\)

\(=\dfrac{xy+y^2+x^2-xy}{x^2-y^2}=\dfrac{x^2+y^2}{x^2-y^2}\)

c: \(\dfrac{x}{2x-6}+\dfrac{9}{2x\left(3-x\right)}\)

\(=\dfrac{x}{2\left(x-3\right)}-\dfrac{9}{2x\left(x-3\right)}\)

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