Question

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

Answer 1

`(3x)/(2x-5)*(-2x+5)/(6x-9x^2)`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `=-1/(2-3x)`

Explanation:

`(3x)/(2x-5)*(-2x+5)/(6x-9x^2)`

Extracting factors to provide equivalent expressions in numerators and denominators:
`color(white)("XXXX")` `= (3x)/(2x-5) * ((-1)(2x-5))/((3x)(2-3x))`

"Cancel" equal terms from numerator and denominator
`color(white)("XXXX")` `= (cancel(3x))/(cancel(2x-5)) * ((-1)(cancel(2x-5)))/((cancel(3x))(2-3x))`

Write in "clean form"
`color(white)("XXXX")` `= (3x)/(2x-5) * ((-1)(2x-5))/((3x)(2-3x))` `=-1/(2-3x)`