Question

Perform the indicated operation to determine if the givensimplification is correct. If it is correct, select TRUE. If it is notcorrect, select FALSE.I + 81I +6+4.22 + 12x + 32I +6

Answer 1

Given:

$\frac{x+8}{x^2+12x+32}\frac{.}{\cdot}\frac{x+6}{x+4}=\frac{1}{x+6}$

By taking LHS:

$\begin{gathered} \frac{x+8}{x^2+12x+32}\frac{.}{\cdot}\frac{x+6}{x+4}=\frac{x+8}{(x+8)(x+4)}\times\frac{x+4}{x+6} \\ \frac{x+8}{x^2+12x+32}\frac{.}{\cdot}\frac{x+6}{x+4}=\frac{(x+8)(x+4)}{(x+8)(x+4)(x+6)} \\ \frac{x+8}{x^2+12x+32}\frac{.}{\cdot}\frac{x+6}{x+4}=\frac{1}{x+6} \\ \frac{x+8}{x^2+12x+32}\frac{.}{\cdot}\frac{x+6}{x+4}=\text{ RHS} \end{gathered}$

True