Answer
$\dfrac{6}{5y^{2}-25y+30}-\dfrac{2}{4y^{2}-8y}=\dfrac{7y+15}{10y(y-3)(y-2)}$
Work Step by Step
$\dfrac{6}{5y^{2}-25y+30}-\dfrac{2}{4y^{2}-8y}$
Take out common factor $5$ from the denominator of the first fraction and common factor $4y$ from the denominator of the second fraction:
$\dfrac{6}{5y^{2}-25y+30}-\dfrac{2}{4y^{2}-8y}=\dfrac{6}{5(y^{2}-5y+6)}-\dfrac{2}{4y(y-2)}=...$
Factor the expression inside the parentheses in the denominator of the first fraction:
$...=\dfrac{6}{5(y-3)(y-2)}-\dfrac{2}{4y(y-2)}=...$
Evaluate the substraction of the two rational expressions:
$...=\dfrac{6(4y)-2(5)(y-3)}{(5)(4y)(y-3)(y-2)}=\dfrac{24y-10y+30}{20y(y-3)(y-2)}=...$
$...=\dfrac{14y+30}{20y(y-3)(y-2)}=...$
Take out common factor $2$ from the numerator and simplify:
$...=\dfrac{2(7y+15)}{20y(y-3)(y-2)}=\dfrac{7y+15}{10y(y-3)(y-2)}$
