How do you add #\frac { 7} { x + 2} + \frac { - 4} { x - 3}#?

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Answer 1 · 2017-10-02T02:41:29

#=(3x-29)/((x+2)(x-3))#

Find the least common denominator which is #(x+2)(x-3)#

Next, we manipulate each fraction

#(7color(red)((x-3)))/((x+2)(x-3))+(-4color(blue)((x+2)))/((x+2)(x-3))#

#=(7x-21)/((x+2)(x-3))+(-4x-8)/((x+2)(x-3))#

#=(7x-21-4x-8)/((x+2)(x-3))#

Identify and combine like terms to simplify:

#=(color(red)(7x)color(blue)(-21)color(red)(-4x)color(blue)(-8))/((x+2)(x-3))#

#=(3x-29)/((x+2)(x-3))#

Answer 2 · 2017-10-02T02:49:52

#(3x-29)/((x+2)(x-3)#

#lcm# for #(x+2) & (x-3)# is #(x+2)*(x-3)#

#(7/(x+2))-(4/(x-3))=((7*(x-3))-(4*(x+2)))/((x+2)*(x-3))#

#=(7x-21-4x-8)/(x^2-x-6)#
#(3x-29)/((x+2)*(x-3))#