How do you add or subtract #(x^2+2x)/(12x+54) - (3-x)/(8x+36)#?

1 Answer
Apr 21, 2018

#(x-1)/12#

Explanation:

Given: #(x^2+2x)/(12x+54) - (3-x)/(8x + 36)#

Factor both numerators and denominators:

#(x^2+2x)/(12x+54) - (3-x)/(8x + 36) = (x(x+2))/(6(2x+9)) - (3-x)/(4(2x+9))#

Find the common denominator and simplify:

#(x(x+2))/(6(2x+9))*(2/2) - (3-x)/(4(2x+9))(*3/3)#

#(2x(x+2))/(12(2x+9)) - (3 (3-x))/(12(2x+9))#

#(2x(x+2) - 3(3-x))/(12(2x+9))#

#(2x^2 + 4x - 9 +3x)/(12(2x+9))#

#(2x^2 + 7x - 9)/(12(2x+9))#

Factor the quadratic in the numerator:
#((2x + 9)(x - 1))/(12(2x+9))#

Cancel any common factors:
#(cancel((2x + 9))(x - 1))/(12cancel((2x+9)))#

# = (x-1)/12#