What is expand (y+(x+y)/x)ln(xy) ?

The solution to expand (y+(x+y)/x)ln(xy) is yln(yx)+ln(yx)+(yln(yx))/x

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expand (y+(x+y)/x)ln(xy)

expand

(y + \frac{x + y}{x}) ln (x y)

y ln (y x) + ln (y x) + \frac{y ln ( y x )}{x}

Solution steps

(y + \frac{x + y}{x}) ln (x y)

= ln (y x) (y + \frac{x + y}{x})

Apply the distributive law:

a (b + c) = ab + a c

a = ln (x y), b = y, c = \frac{x + y}{x}

= ln (x y) y + ln (x y) \frac{x + y}{x}

= y ln (y x) + \frac{x + y}{x} ln (y x)

Simplify

y ln (y x) + \frac{x + y}{x} ln (y x) : y ln (y x) + ln (y x) + \frac{y ln ( y x )}{x}

= y ln (y x) + ln (y x) + \frac{y ln ( y x )}{x}

\frac{7 u ( 4 u - 1 ) ( 3 u - 1 )}{4 u + 5}

- (\frac{x + 1}{( 9 x - 2 ) ( x - 1 )})

(y e^{yz} + \frac{1}{z}) (2)

e^{(2 t)} (sin (2 t) - 1)

2 (x - y + 1)^{2}

What is expand (y+(x+y)/x)ln(xy) ?
The solution to expand (y+(x+y)/x)ln(xy) is yln(yx)+ln(yx)+(yln(yx))/x