Simplify the following:

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2 points
Captionless Image
-5

Option 2

Option 3
5x/x-2÷x/x+2

1 answer

To simplify the expression \( \frac{5x}{x-2} \div \frac{x}{x+2} \), we first rewrite the division as multiplication by the reciprocal:

\[ \frac{5x}{x-2} \div \frac{x}{x+2} = \frac{5x}{x-2} \times \frac{x+2}{x} \]

Next, we can multiply the fractions:

\[ = \frac{5x \cdot (x+2)}{(x-2) \cdot x} \]

Now, simplify the expression. The \( x \) in the numerator and denominator cancels out (provided \( x \neq 0 \)):

\[ = \frac{5(x+2)}{x-2} \]

Now, distribute the \( 5 \):

\[ = \frac{5x + 10}{x-2} \]

Thus, the simplified expression is:

\[ \frac{5x + 10}{x-2} \]

This is the simplest form of the given expression.