Question 181100
<font face="Times New Roman" size="+2">

*[tex \Large \text{          }\math \frac{z}{z+3} = \frac {3z}{5z - 1}]


Cross multiply like any proportion problem:



*[tex \Large \text{          }\math (z)(5z - 1) = (3z)(z + 3) ]


Distribute:


*[tex \Large \text{          }\math 5z^2 - z = 3z^2 + 9z ]


Collect terms on the left:


*[tex \Large \text{          }\math 2z^2 - 10z = 0]


Factor:


*[tex \Large \text{          }\math 2(z)(z - 5) = 0]


Therefore:


*[tex \Large \text{          }\math z = 0]


or


*[tex \Large \text{          }\math z = 5]



Check the answers:


*[tex \Large \text{          }\math \frac{z}{z+3} = \frac {3z}{5z - 1}]


*[tex \Large \text{          }\math \frac{0}{0+3} = \frac {0}{- 1}]  True


*[tex \Large \text{          }\math \frac{5}{5+3} = \frac {3 \times 5}{25 - 1}]  True



John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>