# Rationalize the numerator of your formula?

## Homework Statement

(b) Rationalize the numerator of your formula in (a) to rewrite the expression so that it looks like f(h)/g(h), subject to these two conditions: (1) the numerator f(h)defines a line of slope -1, (2) the function f(h)/g(h) is defined for h=0. When you do this

## Homework Equations

(0.75^1/2) - ((12-4h-h^2)/16)^1/2 / h

## The Attempt at a Solution

To rationalize the numerator I multiplied the numerator and the denominator by the conjugate, which in this case is (0.75^1/2) + ((12-4h-h^2)/16)^1/2. The numerator simplified to h/16 + 4/16.
the denominator simplified to just the conjugate. What did I do wrong?

Thanks,

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

(b) Rationalize the numerator of your formula in (a) to rewrite the expression so that it looks like f(h)/g(h), subject to these two conditions: (1) the numerator f(h)defines a line of slope -1, (2) the function f(h)/g(h) is defined for h=0. When you do this

## Homework Equations

(0.75^1/2) - ((12-4h-h^2)/16)^1/2 / h

## The Attempt at a Solution

To rationalize the numerator I multiplied the numerator and the denominator by the conjugate, which in this case is (0.75^1/2) + ((12-4h-h^2)/16)^1/2. The numerator simplified to h/16 + 4/16.
the denominator simplified to just the conjugate. What did I do wrong?

Thanks,
You really should have the entire numerator in parentheses.
((0.751/2) - ((12-4h-h^2)/16)1/2) / h

or use LaTeX .

##\displaystyle \frac{0.75^{1/2} - ((12-4h-h^2)/16)^{1/2} }{h} ##

What makes you think the result is wrong ? (Well, it isn't quite right but it's close.)