You can put this solution on YOUR website! (~((c))-~(d))/(~(c)+~(d))
Remove the parentheses.
(~(c)-~(d))/(~(c)+~(d))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is ((~(c)-~(d)))/((~(c)-~(d))).
(~(c)-~(d))/(~(c)+~(d))*(~(c)-~(d))/(~(c)-~(d))
Use the difference of squares formula to factor a^(2)-b^(2)=(a-b)(a+b).
((~(c)-~(d))(~(c)-~(d)))/((~(c))^(2)-(~(d))^(2))
Square each of the expressions in the factored denominator.
((~(c)-~(d))(~(c)-~(d)))/(c-(d))
Simplify the rationalized expression.
(c-2~(cd)+d)/(c-(d))
Multiply -1 by the d inside the parentheses.
(c-2~(cd)+d)/(c-d)
Move the term after the radical to the front of the radical (c-2~(cd)+d).
c-2*(d~(cd))/(c-d)
Multiply -2 by d to get -2d.
c-(2d~(cd))/(c-d)
Move the term after the radical to the front of the radical (c-2~(cd)+d).
c-2*(d~(cd))/(c-d)
Multiply -2 by d to get -2d.
c-(2d~(cd))/(c-d)
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of (c-d).
c*(c-d)/(c-d)-(2d~(cd))/(c-d)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (c-d).
(c(c-d))/(c-d)-(2d~(cd))/(c-d)
The numerators of expressions that have equal denominators can be combined. In this case, ((c(c-d)))/((c-d)) and -(2d~(cd))/((c-d)) have the same denominator of (c-d), so the numerators can be combined.
((c(c-d))-2d~(cd))/(c-d)
Simplify the numerator of the expression.
(c^(2)-cd-2d~(cd))/(c-d)
You can put this solution on YOUR website!
The object is to get the radicals out of the denominator.
Multiply NUM and DEN by the conjugate of the DEN,
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Or,
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Which is simpler is up for debate.
