Solve the equation: (2b/b-5)-5=(2/5-b)

Question

help please

Answer 1

(2b / (b - 5)) - 5 = 2 / (5 - b)

 

 

The LCD of the equation is (b - 5)(5 - b).

 

(2b(5 - b) - 5(b - 5)(5 - b)) / (b - 5)(5 - b) = (2(b - 5)) / (b - 5)(5 - b)

 

 

Since we now have common denominators, we only need to equate numerators.

 

2b(5 - b) - 5(b - 5)(5 - b) = 2(b - 5)

 

10b - 2b² - 5(5b - b² - 25 + 5b) = 2b - 10

 

10b - 2b² - 25b + 5b² + 125 - 25b = 2b - 10

 

3b² - 40b + 125 = 2b - 10

 

 

Make the right side of equation equal to zero.

 

3b² - 42b + 135 = 0

 

 

Use the quadratic formula to solve for b.

 

 

b = (42 ± √(1764 - 4(405))) / 6

b = (42 ± 12) / 6

 

b = (42 + 12) / 6            and           b = (42 - 12) / 6

 

b = 9                            and            b = 5

 

 

Finally, plug these values back into the equation to see which to accept as the solution.  The left side and right side of equation must be equal to each other.