Answer
$\displaystyle \frac{x+5y}{3x-y}$
Work Step by Step
Simplifying Rational Expressions
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
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Numerator $:$ search for integer factors of $-10$ whose sum is $+3$...
... these are $-2$ and $+5...$
$x^{2}+3xy-10y^{2} =(x-2y)(x+5y)$
Denominator:
search for integer factors of $3(2)=6$ whose sum is $-7$...
... these are $-6$ and $-1...$
$3x^{2} -7xy+2y^{2}=3x^{2} -6xy-xy+2y^{2}$
$=3x(x-2y)-y(x-2y)$
$=(x-2y)(3x-y)$
Expression = $\displaystyle \frac{(x-2y)(x+5y)}{(x-2y)(3x-y)}$
... divide both with the common factor: $ (x-2y)$
Expression = $\displaystyle \frac{x+5y}{3x-y}$
