Question

Perform the indicated operations and simplify.$\frac{(x+5)(x-3)}{x+2}\cdot \frac{1}{(x+5)(x+2)}$

Short answer

The simplified form of the given expression is $(x-3)$

Step-by-step solution

Rearrange The Expressions

Rearrange the expressions so that the like terms are together. $(x+5)(x-3)\cdot 1÷(x+2)\cdot (x+5)(x+2)$

Simplify the Common Terms

Observe that the term $(x+5)$ and $x+2$ is common in the numerator and the denominator of the expression. By the divisional property of equality, we can divide the common terms. Hence the expression becomes $(x-3)$.

Final Result

The final simplified expression is $(x-3)$. No additional simplification can be done, so this is the final result.