Question

Which shows the rational expression written using the least common denominator? X+1/4x^2+x+1/x^2

Answer 1

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Answer 2

The rational expression
`(x + 1)/(4x^2) + (x + 1)/(x^2)` using the least common denominator is
`(5 + 5x)/(4x^2)`

How to express the rational expression using the least common denominator?

From the question, we have the following parameters that can be used in our computation:

`(x + 1)/(4x^2) + (x + 1)/(x^2)`

Take the LCM of the expression

So, we have

`(x + 1)/(4x^2) + (x + 1)/(x^2) = (x + 1 + 4(x + 1))/(4x^2)`

Expand the bracket

`(x + 1)/(4x^2) + (x + 1)/(x^2) = (x + 1 + 4x + 4)/(4x^2)`

So, we have

`(x + 1)/(4x^2) + (x + 1)/(x^2) = (5 + 5x)/(4x^2)`

Hence, the rational expression using the least common denominator is
`(x + 1)/(4x^2) + (x + 1)/(x^2) = (5 + 5x)/(4x^2)`