Question

\(\dfrac{x+1}{2x-2}+\dfrac{-2x}{x^2-1}\)

\(\dfrac{y-12}{6y-36}+\dfrac{4}{y^2-6y}\)

\(\dfrac{6-x}{x^2+3x}+\dfrac{3}{2x+6}\)

Answer 1

\(a,\dfrac{x+1}{2x-2}+\dfrac{-2x}{x^2-1}=\dfrac{x+1}{2.\left(x-1\right)}+\dfrac{-2x}{\left(x+1\right).\left(x-1\right)}=\dfrac{\left(x+1\right).\left(x+1\right)}{2.\left(x-1\right).\left(x+1\right)}+\dfrac{\left(-2x\right).x}{x.\left(x+1\right).\left(x-1\right)}=\dfrac{\left(x+1\right).\left(x+1\right)-2x^2}{x.\left(x+1\right)\left(x-1\right)}\)

Answer 2

b: \(=\dfrac{y^2-12y+24}{6y\left(y-6\right)}\)

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