Multiplying Fractions With Negatives: (-3/4)[(4+sqrt{2})/(-9+6 sqrt{3})]

[Ted_Grendy]

Hello all

I was wondering if someone could help shed light on how to solve the fraction below, I keep getting confused because of the negative 3/4, can anyone help.

. . . . .\(\displaystyle \left(-\dfrac{3}{4}\right)\, \times\, \left(\dfrac{4\, +\, \sqrt{\strut 2\,}}{-9\, +\, 6\, \sqrt{\strut 3\,}}\right)\)

Thank you

 

[Harry_the_cat]

\(\displaystyle -\frac {3}{4} = \frac{-3}{4} = \frac {3}{-4}\)

 

[pka]

Hello all
I was wondering if someone could help shed light on how to solve the fraction below, I keep getting confused because of the negative 3/4, can anyone help.

\(\displaystyle \left( { - \dfrac{3}{4}} \right)\dfrac{{4 + \sqrt 2 }}{{ - 9 + 6\sqrt 3 }} = \left( {\dfrac{3}{4}} \right)\dfrac{{4 + \sqrt 2 }}{{9 - 6\sqrt 3 }}\)

 

[Dr.Peterson]

I was wondering if someone could help shed light on how to solve the fraction below, I keep getting confused because of the negative 3/4, can anyone help.

The most important question is, what do you mean by "solve"?

Possibly you mean "rationalize the denominator and simplify", though we don't use the word "solve" for that.

If so, first simplify the second fraction (using the conjugate of the denominator) and the rest will be easier. Show your work, and we can help you with whatever is really stopping you from continuing. The -3/4 can be the last thing you do.