working w/ rtnl exponents: 30(x^2+1)^1/2-30x^2(x^2+1)^(-1/2)

[bluewhale210]

i know how to do this easy problem

a^2x^(1/2)-ax^(1/2)-30x^(1/2)

the anwser to that is

x^(1/2)(a-6)(a+5)

and i get this problem

(-1/2)x^(1/2)-(3/2)x^(-1/2)-6x^(-3/2)

the answer for that is ((-1/2x^(-3/2)(x^2+3x+12))/x^(3/2)

but my problem is this

30(x^2+1)^1/2-30x^2(x^2+1)^(-1/2)

i think u have to pull out the p^2and the ^(-1/2) but i am not sure. i am trying to factor the expression and simplify comletly please help if u can even if it just a thought

 

[skeeter]

30(x^2 + 1)^(1/2) - 30x^2(x^2 + 1)^(-1/2)

factor \(\displaystyle \L 30(x^2 + 1)^{-\frac{1}{2}}\) from both terms ...

\(\displaystyle \L 30(x^2 + 1)^{-\frac{1}{2}}[(x^2 + 1) - x^2] =\)

\(\displaystyle \L 30(x^2 + 1)^{-\frac{1}{2}}[1] =\)

\(\displaystyle \L 30(x^2 + 1)^{-\frac{1}{2}}=\)

\(\displaystyle \L \frac{30}{\sqrt{x^2+1}}\)

 

[soroban]

Re: i still cant furgure how to work factoring with rational

Hello, bluewhale210!

There are a number of ways . . . skeeter showed you an excellent method.

\(\displaystyle \L30(x^2\,+\,1)^{\frac{1}{2}}\,-\,30x^2(x^2\,+\,1)^{-\frac{1}{2}}\)

[1] We have: \(\displaystyle \: 30\sqrt{x^2\,+\,1}\,-\,\L\frac{30x^2}{\sqrt{x^2\,+\,1}}\)

Get a common denominator ... multiply the first fraction by \(\displaystyle \frac{\sqrt{x^2\,+\,1}}{\sqrt{x^2\,+\,1}}\)

. . \(\displaystyle \L\:\frac{\sqrt{x^2\,+\,1}}{\sqrt{x^2\,+\,1}}\cdot\frac{30\sqrt{x^2\,+\,1}}{1} \,-\,\frac{30x^2}{\sqrt{x^2\,+\,1}} \:=\:\frac{30(x^2\,+\,1)}{\sqrt{x^2\,+\,1}} - \frac{30x^2}{\sqrt{x^2\,+\,1}}\)

. . \(\displaystyle \L=\;\frac{30(x^2\,+\,1)\,-\,30x^2}{\sqrt{x^2\,+\,1}} \;=\;\frac{30x^2\,+\,30\,-\,30x^2}{\sqrt{x^2\,+\,1}} \;=\;\fbox{\frac{30}{\sqrt{x^2\,+\,1}}}\)


[2] Multiply by \(\displaystyle \frac{(x^2\,+\,1)^{\frac{1}{2}}}{(x^2\,+\,1)^{\frac{1}{2}}}\)

. . \(\displaystyle \L\frac{(x^2\,+\,1)^{\frac{1}{2}}}{(x^2\,+\,1)^{\frac{1}{2}}}\,\cdot\,\left[ \frac{30(x^2\,+\,1)^{\frac{1}{2}} \,-\,30x^2(x^2\,+\,1)^{-\frac{1}{2}}}{1}\right] \;= \;\frac{30(x^2\,+\,1)\,-\,30x^2}{(x^2\,+\,1)^{\frac{1}{2}}}\)

. . \(\displaystyle \L= \;\frac{30x^2\,+\,30\,-\,30x^2}{(x^2\,+\,1)^{\frac{1}{2}}} \;=\;\fbox{\frac{30}{(x^2\,+\,1)^{\frac{1}{2}}}}\)

 

[bluewhale210]

thank you all for the help you both been every helpful