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

Question

Eva Adamson · Accepted Answer

#(x-1)/12#

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#

Hazel Anglin · Answer

undefined To add or subtract the given expressions, we need to find a common denominator. In this case, the common denominator is (12x+54)(8x+36).

To subtract the fractions, we multiply the numerator and denominator of each fraction by the common denominator.

For the first fraction, (x^2+2x)/(12x+54), we multiply the numerator and denominator by (8x+36).

For the second fraction, (3-x)/(8x+36), we multiply the numerator and denominator by (12x+54).

After multiplying, we simplify the expressions and combine like terms in the numerator.

Finally, we subtract the second fraction from the first fraction and simplify the resulting expression if necessary.