# How do you simplify  ((3x)/y -x/1) / ((2y)/1 - y/x)?

Mar 24, 2018

$\frac{\left(3 \frac{x}{y}\right) - \left(\frac{x}{1}\right)}{\left(2 \frac{y}{1}\right) - \left(\frac{y}{x}\right)} = \frac{{x}^{2} \left(3 - y\right)}{{y}^{2} \left(2 x - 1\right)}$

#### Explanation:

[0]$\frac{\left(3 \frac{x}{y}\right) - \left(x \cdot \frac{y}{1 \cdot y}\right)}{\left(2 y \cdot \frac{x}{1 \cdot x}\right) - \left(\frac{y}{x}\right)} = \frac{\left(3 \frac{x}{y}\right) - \left(x \frac{y}{y}\right)}{\left(2 x \frac{y}{x}\right) - \left(\frac{y}{x}\right)}$
[1]$\frac{\frac{3 x - x y}{y}}{\frac{2 x y - y}{x}}$
When you divided, you can also say that you multiply by the inverse.
[2]$\frac{x \left(3 - y\right)}{y} \cdot \frac{x}{y \left(2 x - 1\right)}$
[3]$\frac{{x}^{2} \left(3 - y\right)}{{y}^{2} \left(2 x - 1\right)}$