SOLVING RATIONAL EQUATIONS WITH FACTORING

Problem 1 :

Solution :

By using cross multiplication we get,

1 + b = 6

b = 6 - 1

b = 5

Problem 2 :

Solution :

By using cross multiplication we get,

b + 12 = 2(b + 4)

b + 12 = 2b + 8

2b - b = 12 - 8

b = 4

Problem 3 :

Solution :

4v + 7 = 7v - 56

7v - 4v = 7 + 56

3v = 63

v = 63/3

v = 21

Problem 4 :

Solution :

By using cross multiplication we get,

1 + m - 1 = 5

m = 5

Problem 5 :

Solution :

By using cross multiplication we get,

r - 4 = 6(r - 5)

r - 4 = 6r - 30

6r - r = -4 + 30

5r = 26

r = 26/5

Problem 6 :

Solution :

By using cross multiplication we get,

v - 4 = 8v - 40

8v - v = -4 + 40

7v = 36

v = 36/7

Problem 7 :

Solution :

By using cross multiplication we get,

3x + x² - 5x - 24 = x - 6

x² - 2x - 24 = x - 6

x² - 2x - 24 - x + 6 = 0

x² - 3x - 18 = 0

By using algebraic expression.

x² - 6x + 3x - 18 = 0

x(x - 6) + 3(x - 6) = 0

(x + 3) and (x - 6) = 0

x + 3 = 0 and x - 6 = 0

x = -3, x = 6

Problem 8 :

Solution :

By using cross multiplication we get,

x² + 2x = 1 + (x - 1)(x + 2)

x² + 2x = 1 + x² + 2x - x - 2

x² + 2x - 1 - x² - 2x + x + 2 = 0

-1 + x + 2 = 0

x + 1 = 0

x = -1