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$3xy=4xz=5yz$

$ {x+y \over x-z}=?$

The answer is ${9 \over 2}$

But how to solve?

I am preparing for exam.

This question comes from metropol mathematics 1 testbook

black
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3 Answers3

2

$x=\frac{5y}{4}$ and $z=\frac{3y}{4}$

Does this help?

Fareed Abi Farraj
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    The answer is ${9 \over 2}$ – black Nov 28 '19 at 19:53
  • @black Assume $y \neq 0$ and use those $2$ values in the fraction, remove the common factor of $y$ in the numerator & denominator, then what do you get after you otherwise simplify the result? – John Omielan Nov 28 '19 at 19:57
  • @JohnOmielan I get 4 – black Nov 28 '19 at 20:06
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    @black You must've made a mistake. Note $x + y = \frac{5y}{4} + \frac{4y}{4} = \left(\frac{9}{4}\right)y$ and $x - z = \frac{5y}{4} - \frac{3y}{4} = \left(\frac{2}{4}\right)y$. – John Omielan Nov 28 '19 at 20:23
1

Suppose

$$3xy=4xz=5yz$$

then

$$3xy=4xz \implies y=\frac{4z}{3}=\frac{4x}{5}$$ $$4xz=5yz \implies x=\frac{5y}{4}=\frac{5z}{3}$$ $$3xy=5yz \implies z=\frac{3x}{5}=\frac{3y}{4}$$

and

$$x+y=x+\frac{4x}{5}=\frac{9x}{5}$$ $$x-z=x-\frac{3x}{5}=\frac{2x}{5}$$

so provided $x\neq 0$

$$\frac{x+y}{x-z}={\frac{45x}{10x}}=\frac{9}{2}$$

Axion004
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There is no single answer without additional restrictions on $x,y,z$. First we notice that if a constant in each of the three expressions is considered a missing variable, we quickly get a solution $z=3,y=4,x=5$, then the answer would be $(x+y)/(x-z)=9/2.$ But notice that $x=1,y=0,z=0$ is also a solution, but then $(x+y)/(x-z)=1$.

Sil
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