# How do you solve 3/(2y-7) = 3/y?

Jul 16, 2016

Clear the fractions and solve a 2-step equation to get a solution of $y = 7$.

#### Explanation:

We first want to clear the fraction on the left side of the equation. We do that by multiplying by $2 y - 7$:
$\frac{3}{2 y - 7} = \frac{3}{y}$

$\to \frac{3}{2 y - 7} \left(2 y - 7\right) = \frac{3}{y} \left(2 y - 7\right)$

$\to \frac{3}{\cancel{\left(2 y - 7\right)}} \cancel{\left(2 y - 7\right)} = \frac{3}{y} \left(2 y - 7\right)$

$\to 3 = \frac{3 \left(2 y - 7\right)}{y}$

Now we clear the $y$ from the right, by multiplying by $y$:
$3 = \frac{3 \left(2 y - 7\right)}{y}$

$\to 3 \cdot y = \frac{3 \left(2 y - 7\right)}{y} \cdot y$

$\to 3 \cdot y = \frac{3 \left(2 y - 7\right)}{\cancel{y}} \cdot \cancel{y}$

$\to 3 y = 3 \left(2 y - 7\right)$

Distributing the $3$ on the right gives us:
$3 y = 3 \left(2 y - 7\right)$
$\to 3 y = 6 y - 21$

Now we just have to solve this two-step equation, and we have $y$:
$3 y = 6 y - 21$

$\to - 3 y = - 21$

$\to y = \frac{- 21}{-} 3 = 7$