What is x/y+y/z+z/x ?

The solution to x/y+y/z+z/x is (x^2z+xy^2+yz^2)/(xyz)

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simplify x/y+y/z+z/x

simplify

\frac{x}{y} + \frac{y}{z} + \frac{z}{x}

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

Solution steps

\frac{x}{y} + \frac{y}{z} + \frac{z}{x}

Least Common Multiplier of

y, z, x : x yz

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

x - (5 - 3 x) = 7 x + 4

- 7 = \frac{5 x - 19}{- 3}

8 = 18 - y

11 x^{2} - 37 x = 0

x + 20 + 10 x = 20 + 9 x