SOLUTION: rationalize (28-3(square root 15))/(21+4(square root 15))

Question 430111: rationalize (28-3(square root 15))/(21+4(square root 15))
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
NOTE: ~ STANDS FOR SQUARE ROOT OF
(28-3(~(15)))/(21+4(~(15)))
Multiply 4 by each term inside the parentheses.
(28-3(~(15)))/(21+4~(15))
Multiply -3 by each term inside the parentheses.
(28-3~(15))/(21+4~(15))
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 ((21-4~(15)))/((21-4~(15))).
(28-3~(15))/(21+4~(15))*(21-4~(15))/(21-4~(15))
Use the difference of squares formula to factor a^(2)-b^(2)=(a-b)(a+b).
((28-3~(15))(21-4~(15)))/((21)^(2)-(4~(15))^(2))
Square each of the expressions in the factored denominator.
((28-3~(15))(21-4~(15)))/(441-(240))
Simplify the rationalized expression.
(768-175~(15))/(441-(240))
Multiply -1 by the 240 inside the parentheses.
(768-175~(15))/(441-240)
Subtract 240 from 441 to get 201.
(768-175~(15))/(201)
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