Answer :
To rationalize a denominator that has more than one term, you do not multiply the fraction by [tex]\(\frac{B}{B}\)[/tex], where [tex]\(B\)[/tex] is the conjugate of the numerator.
The correct process is as follows:
To rationalize a denominator that contains more than one term, such as in the expression [tex]\(\frac{1}{a + b\sqrt{c}}\)[/tex], you need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of [tex]\(a + b\sqrt{c}\)[/tex] is [tex]\(a - b\sqrt{c}\)[/tex].
So, you multiply the fraction by:
[tex]\[ \frac{a - b\sqrt{c}}{a - b\sqrt{c}} \][/tex]
This is because multiplying by the conjugate uses the difference of squares formula to eliminate the radical from the denominator:
[tex]\[ (a + b\sqrt{c})(a - b\sqrt{c}) = a^2 - (b\sqrt{c})^2 = a^2 - b^2c \][/tex]
Hence, the statement in the question is incorrect, as you should be using the conjugate of the denominator, not the numerator.
So, the correct answer is:
B. False
The correct process is as follows:
To rationalize a denominator that contains more than one term, such as in the expression [tex]\(\frac{1}{a + b\sqrt{c}}\)[/tex], you need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of [tex]\(a + b\sqrt{c}\)[/tex] is [tex]\(a - b\sqrt{c}\)[/tex].
So, you multiply the fraction by:
[tex]\[ \frac{a - b\sqrt{c}}{a - b\sqrt{c}} \][/tex]
This is because multiplying by the conjugate uses the difference of squares formula to eliminate the radical from the denominator:
[tex]\[ (a + b\sqrt{c})(a - b\sqrt{c}) = a^2 - (b\sqrt{c})^2 = a^2 - b^2c \][/tex]
Hence, the statement in the question is incorrect, as you should be using the conjugate of the denominator, not the numerator.
So, the correct answer is:
B. False
