How do you simplify #\frac { \frac { x } { 2} - \frac { 2} { x } } { \frac { 3} { 2} - \frac { 3} { x } #?

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Answer 1 · 2016-11-28T23:29:41

#(x + 2)/3#

First, you should get each individual fraction over a common denominator, in this case #2x#.

#((x/x)(x/2) - (2/2)(2/x))/((x/x)(3/2)-(2/2)(3/x))#

#(x^2/(2x) - 4/(2x))/((3x)/(2x) - 6/(2x))#

#((x^2 - 4)/(2x))/((3x - 6)/(2x))#

Next, divide the fractions:

#((2x)(x^2 - 4))/((2x)(3x - 6))#

#(x^2 - 4)/(3x - 6)#

Next, factor the numerator and denominator:

#((x - 2)(x + 2))/(3(x - 2)#

#(cancel((x - 2))(x + 2))/(3cancel((x - 2))#

#(x + 2)/3#