What is ((2x))/((3y-3x))+((3y))/((5x-5y)) ?

The solution to ((2x))/((3y-3x))+((3y))/((5x-5y)) is -(10x-9y)/(3(5x-5y))

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simplify ((2x))/((3y-3x))+((3y))/((5x-5y))

simplify

\frac{( 2 x )}{( 3 y - 3 x )} + \frac{( 3 y )}{( 5 x - 5 y )}

- \frac{10 x - 9 y}{3 ( 5 x - 5 y )}

Solution steps

\frac{2 x}{3 y - 3 x} + \frac{3 y}{5 x - 5 y}

Least Common Multiplier of

3 y - 3 x, 5 x - 5 y : (3 y - 3 x) (5 x - 5 y)

Adjust Fractions based on the LCM

= \frac{2 x ( 5 x - 5 y )}{( 3 y - 3 x ) ( 5 x - 5 y )} + \frac{3 y ( 3 y - 3 x )}{( 3 y - 3 x ) ( 5 x - 5 y )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{2 x ( 5 x - 5 y ) + 3 y ( 3 y - 3 x )}{( 3 y - 3 x ) ( 5 x - 5 y )}

Simplify

2 x (5 x - 5 y) + 3 y (3 y - 3 x) : 10 x^{2} - 19 x y + 9 y^{2}

= \frac{10 x ^{2} - 19 x y + 9 y ^{2}}{( 3 y - 3 x ) ( 5 x - 5 y )}

Cancel

\frac{10 x ^{2} - 19 x y + 9 y ^{2}}{( 3 y - 3 x ) ( 5 x - 5 y )} : - \frac{10 x - 9 y}{3 ( 5 x - 5 y )}

= - \frac{10 x - 9 y}{3 ( 5 x - 5 y )}

\frac{1}{( a ^{- 2} + b )}

a^{16} - b^{16}

x^{4} y^{2} + (7 + 5) x^{2} y + 35

d^{4} + 18 d^{2} + 81

\frac{1}{( 1 + x ^{a + b} )} + \frac{1}{( 1 + x ^{b - a} )}

What is ((2x))/((3y-3x))+((3y))/((5x-5y)) ?
The solution to ((2x))/((3y-3x))+((3y))/((5x-5y)) is -(10x-9y)/(3(5x-5y))