# How do you simplify (3x)/(2x-5) * (-2x+5)/(6x-9x^2)?

Jul 16, 2015

$\frac{3 x}{2 x - 5} \cdot \frac{- 2 x + 5}{6 x - 9 {x}^{2}}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= - \frac{1}{2 - 3 x}$

#### Explanation:

$\frac{3 x}{2 x - 5} \cdot \frac{- 2 x + 5}{6 x - 9 {x}^{2}}$

Extracting factors to provide equivalent expressions in numerators and denominators:
$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{3 x}{2 x - 5} \cdot \frac{\left(- 1\right) \left(2 x - 5\right)}{\left(3 x\right) \left(2 - 3 x\right)}$

"Cancel" equal terms from numerator and denominator
$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{\cancel{3 x}}{\cancel{2 x - 5}} \cdot \frac{\left(- 1\right) \left(\cancel{2 x - 5}\right)}{\left(\cancel{3 x}\right) \left(2 - 3 x\right)}$

Write in "clean form"
$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{3 x}{2 x - 5} \cdot \frac{\left(- 1\right) \left(2 x - 5\right)}{\left(3 x\right) \left(2 - 3 x\right)}$$= - \frac{1}{2 - 3 x}$