Let
![a1=768\\a2=480\\a3=300\\a4=187.5](https://tex.z-dn.net/?f=%20a1%3D768%5C%5Ca2%3D480%5C%5Ca3%3D300%5C%5Ca4%3D187.5%20%20%20%20)
Step ![1](https://tex.z-dn.net/?f=%201%20)
Find ![\frac{a2}{a1}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba2%7D%7Ba1%7D%20%20)
![\frac{a2}{a1} =\frac{480}{768}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba2%7D%7Ba1%7D%20%3D%5Cfrac%7B480%7D%7B768%7D%20%20)
Divide by
numerator and denominator
![\frac{480}{768} =\frac{\frac{480}{96}}{\frac{768}{96}} \\ \\ \frac{480}{768}=\frac{5}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B480%7D%7B768%7D%20%3D%5Cfrac%7B%5Cfrac%7B480%7D%7B96%7D%7D%7B%5Cfrac%7B768%7D%7B96%7D%7D%20%5C%5C%20%20%20%5C%5C%20%5Cfrac%7B480%7D%7B768%7D%3D%5Cfrac%7B5%7D%7B8%7D%20%20)
![a2=a1*\frac{5}{8}](https://tex.z-dn.net/?f=%20a2%3Da1%2A%5Cfrac%7B5%7D%7B8%7D%20%20)
Step ![2](https://tex.z-dn.net/?f=%202%20)
Find ![\frac{a3}{a2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba3%7D%7Ba2%7D%20%20)
![\frac{a3}{a2} =\frac{300}{480}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba3%7D%7Ba2%7D%20%3D%5Cfrac%7B300%7D%7B480%7D%20%20)
Divide by
numerator and denominator
![\frac{300}{480} =\frac{\frac{300}{60}}{\frac{480}{60}} \\ \\ \frac{300}{480}=\frac{5}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B300%7D%7B480%7D%20%3D%5Cfrac%7B%5Cfrac%7B300%7D%7B60%7D%7D%7B%5Cfrac%7B480%7D%7B60%7D%7D%20%5C%5C%20%20%20%5C%5C%20%20%5Cfrac%7B300%7D%7B480%7D%3D%5Cfrac%7B5%7D%7B8%7D%20%20)
![a3=a2*\frac{5}{8}](https://tex.z-dn.net/?f=%20a3%3Da2%2A%5Cfrac%7B5%7D%7B8%7D%20%20)
Step ![3](https://tex.z-dn.net/?f=%203%20)
Find ![\frac{a4}{a3}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba4%7D%7Ba3%7D%20%20)
![a4=187.5 \\ a4=187\frac{1}{2} \\ \\ a4=\frac{375}{2}](https://tex.z-dn.net/?f=%20a4%3D187.5%20%5C%5C%20a4%3D187%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%5C%5C%20a4%3D%5Cfrac%7B375%7D%7B2%7D%20%20)
![\frac{a4}{a3} =\frac{\frac{375}{2}}{300} \\ \\ \frac{a4}{a3} =\frac{375}{600}](https://tex.z-dn.net/?f=%20%20%5Cfrac%7Ba4%7D%7Ba3%7D%20%3D%5Cfrac%7B%5Cfrac%7B375%7D%7B2%7D%7D%7B300%7D%20%20%5C%5C%20%5C%5C%20%20%5Cfrac%7Ba4%7D%7Ba3%7D%20%3D%5Cfrac%7B375%7D%7B600%7D%20%20)
Divide by
numerator and denominator
![\frac{375}{600} =\frac{\frac{375}{75}}{\frac{600}{75}} \\ \\ \frac{375}{600}=\frac{5}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B375%7D%7B600%7D%20%3D%5Cfrac%7B%5Cfrac%7B375%7D%7B75%7D%7D%7B%5Cfrac%7B600%7D%7B75%7D%7D%20%5C%5C%20%20%20%5C%5C%20%5Cfrac%7B375%7D%7B600%7D%3D%5Cfrac%7B5%7D%7B8%7D%20%20)
![a4=a3*\frac{5}{8}](https://tex.z-dn.net/?f=%20a4%3Da3%2A%5Cfrac%7B5%7D%7B8%7D%20%20)
In this problem
The geometric sequence formula is equal to
![a(n+1)=a(n)*\frac{5}{8}\\](https://tex.z-dn.net/?f=%20a%28n%2B1%29%3Da%28n%29%2A%5Cfrac%7B5%7D%7B8%7D%5C%5C%20%20)
For ![n\geq 1](https://tex.z-dn.net/?f=%20n%5Cgeq%201%20)
therefore
the answer is
the common ratio for the geometric sequence above is ![\frac{5}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B8%7D%20%20)
No idea what this is, sorry
You would do 5 times 4 which is 20. then count how many zero's there are and put them after the 20.
Answer:
x = - 3 and x = 1
Step-by-step explanation:
Given the rational expression
![\frac{x}{x^2+2x-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%5E2%2B2x-3%7D)
The denominator of the expression cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the values that x cannot be, that is
x² + 2x - 3 = 0 ← in standard form
(x + 3)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 1 = 0 ⇒ x = 1
Thus x = 1 and x = - 3 are both excluded values