How do you solve p/(p-2) - 1/2 = 3/(3p-6)?

2 Answers
Apr 14, 2017

p=0

Explanation:

Find a common denominator.

I can see that 3p-6 is actually 3(p-2) There's also a 2 in 1/2. So a common denominator is 6(p-2)

Take this common denominator and multiply everything by that:

6p-3(p-2)=6

Distribute the 3

6p-3p+6=6

Combine the ps:

3p+6=6

Subtract 6 on both sides:

3p=0

Divide 3 on both sides to solve for p:

p=0

Plug p=0 back into the equation to make sure it works:

(0/(0-2))-(1/2)=3/(3(0)-6)

-1/2=3/-6

Simplifying 3/-6 would get -1/2 so the answer works!

Apr 14, 2017

p = 0

Explanation:

Multiply both sides by 3 p - 6:
1/2 (6 - 3 p) + (p (3 p - 6))/(p - 2) = 3

Rewrite the left hand side by combining fractions. 1/2 (6 - 3 p) + (p (3 p - 6))/(p - 2) = (3 (p + 2))/2:

(3 (p + 2))/2 = 3

Multiply both sides by 2/3:
p + 2 = 2

Subtract 2 from both sides:
Answer:
p = 0