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

Apr 14, 2017

$p = 0$

#### Explanation:

Find a common denominator.

I can see that $3 p - 6$ is actually $3 \left(p - 2\right)$ There's also a $2$ in $\frac{1}{2}$. So a common denominator is $6 \left(p - 2\right)$

Take this common denominator and multiply everything by that:

$6 p - 3 \left(p - 2\right) = 6$

Distribute the $3$

$6 p - 3 p + 6 = 6$

Combine the $p$s:

$3 p + 6 = 6$

Subtract $6$ on both sides:

$3 p = 0$

Divide $3$ on both sides to solve for $p$:

$p = 0$

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

$\left(\frac{0}{0 - 2}\right) - \left(\frac{1}{2}\right) = \frac{3}{3 \left(0\right) - 6}$

$- \frac{1}{2} = \frac{3}{-} 6$

Simplifying $\frac{3}{-} 6$ would get $- \frac{1}{2}$ so the answer works!

Apr 14, 2017

$p = 0$

#### Explanation:

Multiply both sides by $3 p - 6$:
$\frac{1}{2} \left(6 - 3 p\right) + \frac{p \left(3 p - 6\right)}{p - 2} = 3$

Rewrite the left hand side by combining fractions. $\frac{1}{2} \left(6 - 3 p\right) + \frac{p \left(3 p - 6\right)}{p - 2} = \frac{3 \left(p + 2\right)}{2}$:

$\frac{3 \left(p + 2\right)}{2} = 3$

Multiply both sides by $\frac{2}{3}$:
$p + 2 = 2$

Subtract 2 from both sides:
$p = 0$