[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
_____________ multiply thru and add
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
__________________ add fractions
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