[addition of rational expessions 2][section 56]

2x
(1.)  7 +  _______                here is the problem
y + z

7(y + z)      2x          multiply 7 by (y+z)/(y+z)
=  ________ + __________
y + z      y + z

=    7y + 7z + 2x
y + z

(2.)   4
______ + 4                     here is the problem
z - 2

4          4(z - 2)     multiply 4 by (z-2)/(z-2)
=   ___________ +  ___________
z - 2          z - 2

=    4 + 4z - 8     multiply thru and add fractions
__________
z - 2

=     4z - 4
______
z - 2          combine like terms

a + b
(3.)    18 - ________              here is the problem
a - b

18(a - b)        a + b        multiply 18 by (a-b)/(a-b)
=   _____________ - ___________
(a - b)       (a - b)

=   18a - 18b - a - b       multiply thru, subtract fractions
___________________
(a - b)

=     17a - 19b
__________
a - b         combine like terms

(4.)   3r2
__________ - 2               here is the problem
r2 - 9

=    3r2        2(r2 - 9)     multiply 2 by (r2 - 9)/(r2 - 9)
________  - _________
r2 - 9        r2 - 9

=    3r2 - 2r2 + 18          multiply thru, subtract fractions
_______________
r2 - 9

=     r2 + 18
____________
r2 - 9               combine like terms

(5.)  (a/x) - (a - 1)          here is the problem

=     a     x(a - 1)        multiply (a - 1) by x/x
___ - _________
x       x

=   a - ax + x          multiply thru subtract fractions
____________
x

(6.)    5
______ - (t - 1)     here is the problem
r - 1

5        (t - 1)(r - 1)      multiply (t - 1)
=  __________ - ______________     by (r - 1)/(r - 1)
r - 1           r - 1

=     5 - rt + t + r - 1       multiply thru
______________________  subtract fractions
r - 1

2x + 3y
(7.)   2 + __________              here is the problem
x + y

2(x + y)      2x + 3y         multiply 2 by (x+y)/(x+y)
= __________ + __________
x + y          x + y

=   2x + 2y + 2x + 3y     multiply thru parentheses
x + y

=   4x + 5y         combine like terms
_______
x + y

x
(8.)  (x - 5) - ________            here is the problem
x + 3

(x - 5)(x + 3)          x          multiply (x - 5)
=  _________________  - ___________    by (x+3)/(x+3)
x + 3              x + 3

=     x2 + 3x - 5x - 15 - x       foil multiply
________________________    subtract fractions
x + 3

=     x2 - 3x - 15
_______________    combine like terms
x + 3

1
(9.)   a + ___________            here is the problem
a + 1

a(a + 1)           1        multiply a by (a+1)/(a+1)
=  _____________ + ____________
a + 1           a + 1

=    a2 + a + 1           multiply thru add fractions
__________
a + 1

(10.)    3 + (a/b)               here is the problem

3(b/b) + (a/b)             multiply 3 by (b/b)

=    (3b + a)/b          multiply, add fractions