Simplify (x+5)/(3x+12)-(x-4)/(4x+16)

x+53x+12-x-44x+16
Simplify each term.
Factor 3 out of 3x+12.
Factor 3 out of 3x.
x+53(x)+12-x-44x+16
Factor 3 out of 12.
x+53x+3⋅4-x-44x+16
Factor 3 out of 3x+3⋅4.
x+53(x+4)-x-44x+16
x+53(x+4)-x-44x+16
Factor 4 out of 4x+16.
Factor 4 out of 4x.
x+53(x+4)-x-44(x)+16
Factor 4 out of 16.
x+53(x+4)-x-44x+4⋅4
Factor 4 out of 4x+4⋅4.
x+53(x+4)-x-44(x+4)
x+53(x+4)-x-44(x+4)
x+53(x+4)-x-44(x+4)
To write x+53(x+4) as a fraction with a common denominator, multiply by 44.
x+53(x+4)⋅44-x-44(x+4)
To write -x-44(x+4) as a fraction with a common denominator, multiply by 33.
x+53(x+4)⋅44-x-44(x+4)⋅33
Write each expression with a common denominator of 12(x+4), by multiplying each by an appropriate factor of 1.
Multiply x+53(x+4) and 44.
(x+5)⋅43(x+4)⋅4-x-44(x+4)⋅33
Multiply 4 by 3.
(x+5)⋅412(x+4)-x-44(x+4)⋅33
Multiply x-44(x+4) and 33.
(x+5)⋅412(x+4)-(x-4)⋅34(x+4)⋅3
Multiply 3 by 4.
(x+5)⋅412(x+4)-(x-4)⋅312(x+4)
(x+5)⋅412(x+4)-(x-4)⋅312(x+4)
Combine the numerators over the common denominator.
(x+5)⋅4-(x-4)⋅312(x+4)
Simplify the numerator.
Apply the distributive property.
x⋅4+5⋅4-(x-4)⋅312(x+4)
Move 4 to the left of x.
4⋅x+5⋅4-(x-4)⋅312(x+4)
Multiply 5 by 4.
4⋅x+20-(x-4)⋅312(x+4)
Apply the distributive property.
4x+20+(-x–4)⋅312(x+4)
Multiply -1 by -4.
4x+20+(-x+4)⋅312(x+4)
Apply the distributive property.
4x+20-x⋅3+4⋅312(x+4)
Multiply 3 by -1.
4x+20-3x+4⋅312(x+4)
Multiply 4 by 3.
4x+20-3x+1212(x+4)
Subtract 3x from 4x.
x+20+1212(x+4)
Add 20 and 12.
x+3212(x+4)
x+3212(x+4)
Simplify (x+5)/(3x+12)-(x-4)/(4x+16)