What is expand (ax+y+sqrt((ax+y)^2+z^2))/z ?

The solution to expand (ax+y+sqrt((ax+y)^2+z^2))/z is (ax)/z+y/z+(sqrt(a^2x^2+2axy+y^2+z^2))/z

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expand (ax+y+sqrt((ax+y)^2+z^2))/z

expand

\frac{a x + y + ( a x + y ) ^{2} + z ^{2}}{z}

\frac{a x}{z} + \frac{y}{z} + \frac{a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

Solution steps

\frac{a x + y + ( a x + y ) ^{2} + z ^{2}}{z}

Expand

(a x + y)^{2} + z^{2} : a^{2} x^{2} + 2 a x y + y^{2} + z^{2}

= \frac{a x + y + a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

Apply the fraction rule:

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

\frac{a x + y + a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z} = \frac{a x}{z} + \frac{y}{z} + \frac{a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

= \frac{a x}{z} + \frac{y}{z} + \frac{a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

, (3 - 9) (3 - 5)

\frac{( x - 1 ) ^{3}}{x}

(e^{x} + e^{x} x) \cdot e^{x}

(\frac{3}{4} - 7 m) (\frac{3}{4} + 7 m)

\frac{2}{s ( s ^{2} + 7 s + 12 )} + \frac{e ^{- 2 s}}{s ^{2} + 7 s + 12}

What is expand (ax+y+sqrt((ax+y)^2+z^2))/z ?
The solution to expand (ax+y+sqrt((ax+y)^2+z^2))/z is (ax)/z+y/z+(sqrt(a^2x^2+2axy+y^2+z^2))/z