How do you add #\frac { 4} { ( x + 3) ( x + 2) } + \frac { 16} { ( x + 2) ( x - 2) }#?

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Answer 1 · 2018-05-19T05:13:07

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

or

#(20)/(x^2 + x -6)#

#4/((x+3)(x+2))+16/((x+2)(x-2))#

First find a common denominator, it must have all the factors of both denominators:

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

Then we have to multiply the missing factor times each term:

#(4(x-2))/((x+3)(x+2)(x-2))+(16(x+3))/((x+3)(x+2)(x-2))#

#(4x-8 +16x +48)/((x+3)(x+2)(x-2))#

#(20x+40)/((x+3)(x+2)(x-2))#

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

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