Question 5
Rationalise the denominator of
$$\frac1{\sqrt6-\sqrt3+\sqrt2+1}.$$
The printed source offers the following expressions, retained unchanged for comparison:
- A. $\dfrac{\sqrt6+\sqrt3-\sqrt2+1}{2}$
- B. $\dfrac{\sqrt6-\sqrt3+\sqrt2+1}{2}$
- C. $\sqrt6-\sqrt3+\sqrt2+1$
- D. $\sqrt6+\sqrt3-\sqrt2+1$
- E. $\sqrt6-\sqrt3-\sqrt2+1$
For this edition, submit your rationalised expression rather than an option letter. Write the result as $(a+b\sqrt2+c\sqrt3+d\sqrt6)/e$, where the five coefficients are integers with no common factor greater than 1 and $e>0$. Enter a;b;c;d;e in that order, separated by semicolons, with no spaces. Keep every sign, including negative coefficients.
$$\frac1{\sqrt6-\sqrt3+\sqrt2+1}.$$
The printed source offers the following expressions, retained unchanged for comparison:
- A. $\dfrac{\sqrt6+\sqrt3-\sqrt2+1}{2}$
- B. $\dfrac{\sqrt6-\sqrt3+\sqrt2+1}{2}$
- C. $\sqrt6-\sqrt3+\sqrt2+1$
- D. $\sqrt6+\sqrt3-\sqrt2+1$
- E. $\sqrt6-\sqrt3-\sqrt2+1$
For this edition, submit your rationalised expression rather than an option letter. Write the result as $(a+b\sqrt2+c\sqrt3+d\sqrt6)/e$, where the five coefficients are integers with no common factor greater than 1 and $e>0$. Enter a;b;c;d;e in that order, separated by semicolons, with no spaces. Keep every sign, including negative coefficients.