Question

Simplify the following:
*
2 points
Captionless Image
-5

Option 2

Option 3
5x/x-2÷x/x+2

Answer 1

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.