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Please help me rationalize the numerator.

((3x)(3x+h))h

 

The back of the book answer is 3(x×(x+h)+x×x+h)

 

I have tried but cannot seem to get the answer. I believe I am having a simplifying problem, but if anyone can show me steps, that would be highly appriciated. 

 Jul 15, 2015

Best Answer 

 #1
avatar+23254 
+5

I would do it in two steps:

First:  multiply the numerator and denominator by the common denominator:  

             (√(x + h))·(√x)

Giving:

[ 3√(x + h) + 3√x ] / [ h·√(x + h)·√x ]

and factor out the 3:  3[√(x + h) + √x ] / [ h·√(x + h)·√x ]

Now, multiply the numerator and denominator of this fraction by the conjugate of the numerator:

              √(x + h) - √x 

Numerator:  the product of 3[√(x + h) + √x ] times [ √(x + h) - √x  ]  

                    =  3[ (x + h) - x ]  =  3h

Denominator:  the product of [ h·√(x + h)·√x ] times [ √(x + h) - √x  ]  

                    =  h(x+h)√x  - h√(x + h)·x    =  h[ (x+h)√x  - √(x + h)·x ]

                    =  h[ √x(x + h) - x√(x + h) ]

Cancelling the h from both the numerator and the denominator gives you their answer.

 Jul 16, 2015
 #1
avatar+23254 
+5
Best Answer

I would do it in two steps:

First:  multiply the numerator and denominator by the common denominator:  

             (√(x + h))·(√x)

Giving:

[ 3√(x + h) + 3√x ] / [ h·√(x + h)·√x ]

and factor out the 3:  3[√(x + h) + √x ] / [ h·√(x + h)·√x ]

Now, multiply the numerator and denominator of this fraction by the conjugate of the numerator:

              √(x + h) - √x 

Numerator:  the product of 3[√(x + h) + √x ] times [ √(x + h) - √x  ]  

                    =  3[ (x + h) - x ]  =  3h

Denominator:  the product of [ h·√(x + h)·√x ] times [ √(x + h) - √x  ]  

                    =  h(x+h)√x  - h√(x + h)·x    =  h[ (x+h)√x  - √(x + h)·x ]

                    =  h[ √x(x + h) - x√(x + h) ]

Cancelling the h from both the numerator and the denominator gives you their answer.

geno3141 Jul 16, 2015

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