Adding fractions with different exponents

[KidInkFan]

I hope this is under the right section

my questions is:

1. ((1/7)x^(3/2))+((7/2)x^(1/2))=0

I just need help starting the question off i know you need same exponents, but how do you get them to be the same? I know you got to have the same base as well in order to add the fractions.

Thanks for anyones helps towards this question!!

 

[soroban]

Hello, KidInkFan!

\(\displaystyle \text{1. Solve for }x\!:\;\;\frac{1}{7}x^{\frac{3}{2}} + \frac{7}{2}x^{\frac{1}{2}} \:=\:0\)

First, note that \(\displaystyle x \ge 0.\)


Factor: .\(\displaystyle x^{\frac{1}{2}}\left(\frac{1}{7}x + \frac{7}{2}\right) \:=\:0 \)


Solve the two equations:

. . \(\displaystyle x^{\frac{1}{2}} \:=\:0 \quad\Rightarrow\quad \boxed{x \:=\:0}\)

. . \(\displaystyle \frac{1}{7}x + \frac{7}{2} \:=\:0 \quad\Rightarrow\quad \color{red}{\rlap{///////}}x \:=\:\text{-}\frac{49}{2}\)

 

[KidInkFan]

Sorry I'm still a little lost...

why can't x=(-49/2) cause I am supposed to solve for x. Im sorry if i didnt make that clear. My assignment asks for the value of x.

 

[Deleted member 4993]

Sorry I'm still a little lost...

why can't x=(-49/2) cause I am supposed to solve for x. Im sorry if i didnt make that clear. My assignment asks for the value of x.

(-49/2)^1/2 is not in real domain.

 

[KidInkFan]

Oh right!! Thanks everyone for helping me out!! I was able to solve the second question by following your previous steps above