Algebra 2 equation, only need answer

Question

p+x/x-2=a/b

 

Solve for X. Express your answer as a simple fraction in lowest terms

Answer 1

The problem as stated has no solution for x.

 

p + x/x - 2 = a / b

p + 1 -2 = a / b

p - 1 = a / b

 

Strictly solving for x

 

a = b(p-1) ; bx ≠ 0

Answer 2

Billy:  You need to include parenthesis to show the grouping...

I believe your equation is actually:

 

(p+x)/(x-2) = a/b

 

Cross multiplying we get:

 

b(p+x) = a(x-2)

bp + bx = ax - 2a

-ax + bx = -2a-bp

(b-a)x = -2a-bp

 

x = (-2a-bp)/(b-a)

 

Or.. if you don't like all the negatives factor it out to give:

 

x = -(2a+bp)/-(a-b) = (2a+bp)/(a-b)