2 Remove redundant information after refactoring OP
source | link

I like using Composition (@*) for this kind of thing. Your expression:

expr=(x \[LeftAngleBracket]x (-x + 
\!\(\*UnderscriptBox[\(\[Sum]\), \(j\)]\)Derivative[1][v][
    y[j]])\[RightAngleBracket])/\[LeftAngleBracket]x^2\
\[RightAngleBracket] + 
\!\(\*UnderscriptBox[\(\[Sum]\), \(j\)]\)Derivative[1][v][y[j]];

expr //TeXForm

$\frac{x \left\langle x \left(\sum _j v'(y(j))-x\right)\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$

Using Composition:

exprterm /. AngleBracket -> AngleBracket @* Expand //TeXForm

$\frac{x \left\langle x \sum _j v'(y(j))-x^2\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$

I like using Composition (@*) for this kind of thing. Your expression:

expr=(x \[LeftAngleBracket]x (-x + 
\!\(\*UnderscriptBox[\(\[Sum]\), \(j\)]\)Derivative[1][v][
    y[j]])\[RightAngleBracket])/\[LeftAngleBracket]x^2\
\[RightAngleBracket] + 
\!\(\*UnderscriptBox[\(\[Sum]\), \(j\)]\)Derivative[1][v][y[j]];

expr //TeXForm

$\frac{x \left\langle x \left(\sum _j v'(y(j))-x\right)\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$

Using Composition:

expr /. AngleBracket -> AngleBracket @* Expand //TeXForm

$\frac{x \left\langle x \sum _j v'(y(j))-x^2\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$

I like using Composition (@*) for this kind of thing:

term /. AngleBracket -> AngleBracket @* Expand //TeXForm

$\frac{x \left\langle x \sum _j v'(y(j))-x^2\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$

1
source | link

I like using Composition (@*) for this kind of thing. Your expression:

expr=(x \[LeftAngleBracket]x (-x + 
\!\(\*UnderscriptBox[\(\[Sum]\), \(j\)]\)Derivative[1][v][
    y[j]])\[RightAngleBracket])/\[LeftAngleBracket]x^2\
\[RightAngleBracket] + 
\!\(\*UnderscriptBox[\(\[Sum]\), \(j\)]\)Derivative[1][v][y[j]];

expr //TeXForm

$\frac{x \left\langle x \left(\sum _j v'(y(j))-x\right)\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$

Using Composition:

expr /. AngleBracket -> AngleBracket @* Expand //TeXForm

$\frac{x \left\langle x \sum _j v'(y(j))-x^2\right\rangle }{\left\langle x^2\right\rangle }+\sum _j v'(y(j))$