document.write( "Question 617254: 1.if 3-√5 divided by 3+2√5=a√5-b,find a and b \n" ); document.write( "

Algebra.Com's Answer #388240 by jsmallt9(3758) $\"\"$ $\"About$

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$\"%283sqrt%285%29%29%2F%282%2B2sqrt%285%29%29\"$
\n" ); document.write( "First let's rationalize the denominator. Rationalizing two-term denominators with square roots takes advantage of the $\"%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2\"$ pattern. The right side, as you can see is a difference of perfect squares. The left side is a product of two-term expressions. The pattern shows us how to take a two-term expression, an (a+b) or (a-b), and turn it into an expression of perfect squares.

\n" ); document.write( "Your denominator is a two-term sum. IOW, an (a+b). To turn it into an expression of perfect squares we need to multiply it by its corresponding (a-b):
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\n" ); document.write( "Multiplying the denominators is easy; just use the pattern. To multiply the numerators we will need to use the distributive property:
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\n" ); document.write( "which simplifies as follows:
\n" ); document.write( " $\"%286sqrt%285%29-6%2A5%29%2F%284-%284%2A5%29%29\"$
\n" ); document.write( " $\"%286sqrt%285%29-30%29%2F%284-%2820%29%29\"$
\n" ); document.write( " $\"%286sqrt%285%29-30%29%2F%28-16%29\"$
\n" ); document.write( "Now we can split the fraction to get the $\"a%2Asqrt%285%29-b\"$ form:
\n" ); document.write( " $\"%286sqrt%285%29%29%2F%28-16%29-%2830%29%2F%28-16%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"%28-3%2F8%29sqrt%285%29-%28%28-15%29%2F8%29\"$
\n" ); document.write( "So $\"a+=+%28-3%29%2F8\"$ and $\"b+=+-15%2F8\"$ \n" ); document.write( "

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