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• The concepts for this exercise are summarized below.
  For a complete discussion, read the text.
• Need some basic practice renaming fractional expressions first?
  Practice with the Form $\,a\cdot\frac{b}{c}$
  More Practice with the Form $\,a\cdot\frac{b}{c}$

It's often necessary to take a somewhat complicated-looking fraction,
like (say) $\,-\frac{5x}{-3}\,$, and rename it.

One popular name is the form $\,kx\,$:   i.e., a number first, and the variable $\,x\,$ last.
In general, it is efficient to make two ‘passes’ through the expression:
figure out the sign (plus or minus) on the first pass, and the size on the second pass: $$ -\frac{5x}{-3}\ \ \overset{\text{first pass, determine plus/minus sign:}}{ \overset{\text{even # of negative factors, so positive}}{\overbrace{\strut\ \ \ =\ \ \ }}} \ \ \frac{5x}{3}\ \ \overset{\text{‘peel off’ the coefficient}}{ \overset{\text{and write it in front}}{\overbrace{\strut\ \ \ =\ \ \ }}} \ \ \underset{k}{\underbrace{\ \frac53\ }} x $$ This exercise gives you practice with this type of renaming.