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