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How do you evaluate #\frac{x}{x(x+1)}\times \frac{1}{(x+1)}#?

Answer 1

Ethan Adkins

#1/(x+1)^2#

#"we can simplify the fraction on the left by "color(blue)"cancelling"# #"the x on the numerator/denominator"#

#rArr(cancel(x)^1)/(cancel(x)^1(x+1))xx1/(x+1)#

#"multiply numerators/denominators together"#

#rArr1/((x+1)(x+1))=1/(x+1)^2#

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Answer 2

Nathan Axel

To evaluate the expression (\frac{x}{x(x+1)} \times \frac{1}{(x+1)}), follow these steps:

Rewrite the expression by canceling common factors between the numerators and denominators.
Simplify the remaining expression.

Given the expression:

(\frac{x}{x(x+1)} \times \frac{1}{(x+1)})

First, cancel the common factor (x+1) from the first fraction's denominator and the second fraction's numerator:

(\frac{x}{x\cancel{(x+1)}} \times \frac{1}{\cancel{(x+1)}})

Now, simplify the expression:

(\frac{x}{x} \times \frac{1}{1})

This simplifies to:

(1 \times 1)

Therefore, the evaluated expression is (1).

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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.