I NEED HELP ACT PRACTICE!!!

[alexboline21]

here is the question. i have the answer i just dont know how to get to the answer

square root of x over x(one fraction) plus + square root of y over y(another fraction)

the answer is square root of x plus square root of y over x times y(one fraction)

 

[JeffWest]

I am going to retype the problem you stated simply to clarify what you are asking.

\(\displaystyle \frac{\sqrt(x)}{x}+\frac{\sqrt(y)}{y}\)

Answer is \(\displaystyle \frac{\sqrt(x)+\sqrt(y)}{xy}\)


So are you attempting to combine the terms?

Could you clarify?

 

[alexboline21]

no i need to know how to simplyfly the first to get to the other one or the book says evaluate

 

[alexboline21]

sorry the x times y on the botton is also in a square root

 

[mmm4444bot]

the book says evaluate

Unless the book provides a number (or another expression) for either symbol x and y, we cannot evaluate any expression containing x and y. "To evaluate" an expression means to write its value after substituting a number or an expression for one or more symbols in the expression.

\(\displaystyle \frac{\sqrt{x}}{x} + \frac{\sqrt{y}}{y} = \frac{\sqrt{x} + \sqrt{y}}{\sqrt{xy}}\)

One way to get this result is to first recognize that each of the two terms on the lefthand side can be viewed as ratios that have had their denominators rationalized.

Therefore, we can unrationalize the denominators.

In other words, \(\displaystyle \; \frac{\sqrt{x}}{x} + \frac{\sqrt{y}}{y} \;\) is the same as \(\displaystyle \; \frac{1}{\sqrt{x}} + \frac{1}{\sqrt{y}}\)

Can you now "see" the common denominator of \(\displaystyle \sqrt{xy}\) ?

Cheers ~ Mark