How do you simplify #y/(2y)+ (y+2)/y#?

Answer 1

Isaiah Anthony

#y/[2y] + [y+2]/y#

#=[y+2(y+2)]/[2y]#

#=[y+2y+4]/[2y]#

#=[3y+4]/[2y]#

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Answer 2

Eva Adamson

#\frac{3y+4}{2y}#

If you multiply and divide by #2# the second fraction we get

#\frac{y}{2y}+\frac{2(y+2)}{2y} = \frac{y+2(y+2)}{2y} = \frac{y+2y+4}{2y}=\frac{3y+4}{2y}#

If you prefer, you can break the fraction in two fraction by writing

#\frac{3y+4}{2y} = \frac{3cancel(y)}{2cancel(y)}+\frac{cancel(4)^2}{cancel(2)y} = \frac{3}[2}+\frac{2}{y}#.

It depends on your idea of "simplifying", as far as I know there is no standard definition for that term. Let me know if I'm wrong!

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Answer 3

Jameson Allen

To simplify the expression y/(2y) + (y+2)/y, we need to find a common denominator and combine the fractions. The common denominator is 2y.

Multiplying the first fraction by y/y and the second fraction by 2/2, we get (y^2)/(2y^2) + (2y+4)/(2y).

Combining the fractions, we have (y^2 + 2y + 4)/(2y^2).

Therefore, the simplified expression is (y^2 + 2y + 4)/(2y^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.