How do you subtract #\frac { 3 c } { c ^ { 2 } + 4 c - 1 2 } - \frac { 2 c - 5 } { c ^ { 2 } + 2 c - 2 4 }#?

1 Answer
George C.
Oct 13, 2016

#(3c)/(c^2+4c-12) - (2c-5)/(c^2+2c-24) = (c^2-3c-10)/(c^3-28c+48)#

Explanation:

Whenever you are adding or subtracting fractions you need a common denominator.

In our case, we start with denominators:

#c^2+4c-12 = (c+6)(c-2)#

#c^2+2c-24 = (c+6)(c-4)#

So the least common multiple is:

#(c+6)(c-2)(c-4) = c^3-28c+48#

Then:

#(3c)/(c^2+4c-12) - (2c-5)/(c^2+2c-24) = (3c(c-4)-(2c-5)(c-2))/(c^3-28c+48)#

#color(white)((3c)/(c^2+4c-12) - (2c-5)/(c^2+2c-24)) = ((3c^2-12c)-(2c^2-9c+10))/(c^3-28c+48)#

#color(white)((3c)/(c^2+4c-12) - (2c-5)/(c^2+2c-24)) = (c^2-3c-10)/(c^3-28c+48)#

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