How do you solve p/(p-2) - 1/2 = 3/(3p-6)pp−2−12=33p−6?

2 Answers
Astralboy
Apr 14, 2017

p=0p=0

Explanation:

Find a common denominator.

I can see that 3p-63p−6 is actually 3(p-2)3(p−2) There's also a 22 in 1/212. So a common denominator is 6(p-2)6(p−2)

Take this common denominator and multiply everything by that:

6p-3(p-2)=66p−3(p−2)=6

Distribute the 33

6p-3p+6=66p−3p+6=6

Combine the pps:

3p+6=63p+6=6

Subtract 66 on both sides:

3p=03p=0

Divide 33 on both sides to solve for pp:

p=0p=0

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

(0/(0-2))-(1/2)=3/(3(0)-6)(00−2)−(12)=33(0)−6

-1/2=3/-6−12=3−6

Simplifying 3/-63−6 would get -1/2−12 so the answer works!

Andrés G.
Apr 14, 2017

p = 0p=0

Explanation:

Multiply both sides by 3 p - 63p−6:
1/2 (6 - 3 p) + (p (3 p - 6))/(p - 2) = 312(6−3p)+p(3p−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))/212(6−3p)+p(3p−6)p−2=3(p+2)2:

(3 (p + 2))/2 = 33(p+2)2=3

Multiply both sides by 2/323:
p + 2 = 2p+2=2

Subtract 2 from both sides:
Answer:
p = 0p=0

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