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

Question

can someone do this please?

Answer 1

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

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

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

(10b-2b^2-2b+10)/(5b-b^2-25+5b) = 5

(-2b^2+8b+10)/(-b^2+10b-25) = 5

 

now factorize

 

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

 

(b-5) s cancel each other out in the numerator and denominator

 

so we end up with

 

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

 

multiply each side by (-b+5)

 

-2b-2 = -5b + 25

 

now it is a simple linear equation

 

move the variable, b, to one side

 

3b = 27

 

b = 9