documentclass[11pt]{article}
pagestyle{empty}
usepackage{amsmath}
usepackage{xcolor}
newcommand{redx}{{color{red}x}}
newcommand{bluex}{{color{blue}x}}
begin{document}

begin{align}
  x &= biggl[ x frac{frac{y}{z}}{frac{x}{y}} notag \
    & quad quad  + redx frac{frac{y}{z}}{frac{x}{y}}biggr]
end{align}

begin{align}
  x &= left[ x frac{frac{y}{z}}{frac{x}{y}} right.notag \
    & quad quad left. + bluex frac{frac{y}{z}}{frac{x}{y}}right]
end{align}


end{document}

documentclass[11pt]{article}
pagestyle{empty}
usepackage{amsmath}
usepackage{xcolor}
newcommand{redx}{{color{red}x}}
newcommand{bluex}{{color{blue}x}}
begin{document}

begin{align}
  x &= biggl[ x frac{frac{y}{z}}{frac{x}{y}} notag \
    & quad quad  + redx frac{frac{y}{z}}{frac{x}{y}}biggr]
end{align}

begin{align}
  x &= left[ x frac{frac{y}{z}}{frac{x}{y}} right.notag \
    & quad quad left.{} + bluex frac{frac{y}{z}}{frac{x}{y}}right]
end{align}


end{document}