I need help solving this radical equation..PLEASE??!?

Question

x^(3/4) + [5/x^(1/4)]

I am supposed to simplify this problem and I know the answer is (x+5)/fourthroot(x) but i dont know how to get this answer...can someone please show me the steps and explain how to get to this answer???...THANKS! :)

Answer 1

write x^(3/4) as x/x^(1/4)

then your expression becomes:

x/x^(1/4)+5/x^(1/4)

there is a common denom so this becomes

[x+5]/x^(1/4)

Answer 2

More detail this time...

Your problem:         x^(3/4) + 5x^(3/4) / x

Common denominator is x, multiply first term by x/x

so we have x[x^(3/4) ]/x+ 5x^(3/4) / x

Combining numerator terms gives

{x[x^(3/4) + 5x^(3/4)]} / x

Take x^(3/4) out of top terms by reverse distribution:

[x^(3/4)](x+5)/x or

Remember 1/x = x^-1

[x^(3/4)](x+5)(x^-1) or

Since (x^a)(x^b)= x^(a+b) we can combine base x terms

Combining (x^3/4)(x^-1) gives x^((3/4)-1)=x^-1/4

(x^-1/4)(x+5)

or Remember x^-1/4 = 1/(x^1/4) since x^-a= 1/x^a

(x+5)/x^(1/4)

Answer 3

Not sure if this is what you want...

x^(3/4) + [5/x^(1/4)]

=x^(3/4) + [5x^(-1/4)]

=x^(-1/4)[x + 5]

=(x+5)/x^(1/4)

Answer 4

you want to eliminate the radical, x^(1/4), in the denominator by multiplying [5/x^(1/4)] by [x^(-1/4)/x^(-1/4)]...that makes the denominator x^0, which equals 1

x^(3/4) + 5 x^(-1/4)

factor out x^(-1/4) because it has the least power

x^(-1/4) [x+5]

since x^(-1/4) also equals [1/x^(1/4)...

[1/x^(1/4)] [x+5]= (x+5)/x^(1/4)