Thread: Rationalizing the Numerator

1) 1/(Square Root of x) - 1 / x - 1

So I multiply both top and bottom by 1/(Square Root of x) + 1 , right? But I don't know what that equals, I just don't know how to multiply them...

2) x(Square Root of x) - 8 / x - 4

Same thing...maybe if I get help on 1 I can get this one.

More questions to come I'm sure...

Originally Posted by Dickson

1) 1/(Square Root of x) - 1 / x - 1



So I multiply both top and bottom by 1/(Square Root of x) + 1 , right? But I don't know what that equals, I just don't know how to multiply them...



2) x(Square Root of x) - 8 / x - 4



Same thing...maybe if I get help on 1 I can get this one.



More questions to come I'm sure...

If you typed more intelligibly, it would be easier t answer you and you would have probably gotten an answer by now.

what you typed can be interpreted several ways, please use parentheses to clarify

i believe the first question is . personally, i'd combine the fractions first, but multiplying by is a valid option.

note that the whole point of multiplying by the conjugate is to obtain the difference of two squares. hence the numerator will change from the form to the form , and we get



now simplify


for the second problem, note that you have

which should remind you of the difference of two cubes formula, which should help you know how to proceed.

Originally Posted by Dickson

1) 1/(Square Root of x) - 1 / x - 1

So I multiply both top and bottom by 1/(Square Root of x) + 1 , right? But I don't know what that equals, I just don't know how to multiply them...

2) x(Square Root of x) - 8 / x - 4

Same thing...maybe if I get help on 1 I can get this one.

More questions to come I'm sure...

Note that the key is knowing the formula:


See if you can take it from here.

yeah i got tha ...i don't know how to multiply the 2 binomials