Simplify the complex fraction using Method 2.
-$\frac { \frac { 1 } { \mathrm { k } + 2 } } { \frac { 5 } { \mathrm { k } ^ { 2 } - 4 } }$
A) $\frac { \mathrm { k } - 2 } { 5 }$
B)k - 2
C) $\frac { 5 } { k - 2 }$
D) $\frac { \mathrm { k } + 2 } { 5 }$

Question

Quizplus · Accepted Answer

To simplify the given complex fraction, we first recognize that $\frac{5}{k^2-4}$ can be simplified by recognizing $k^2-4$ as a difference of squares, $k^2-4=(k+2)(k-2)$. Thus, the complex fraction becomes $\frac{\frac{1}{k+2}}{\frac{5}{(k+2)(k-2)}}$. Simplifying further by multiplying the numerator and denominator by $(k+2)(k-2)$, we get $\frac{(k+2)(k-2)}{5(k+2)}$, which simplifies to $\frac{k-2}{5}$, matching choice A.

Simplify the Complex Fraction Using Method 2 1k+25k2−4\frac { \frac { 1 } { \mathrm { k } + 2 } } { \frac { 5 } { \mathrm { k } ^ { 2 } - 4 } }k2−45​k+21​​

Simplify the Complex Fraction Using Method 2 $\frac { \frac { 1 } { \mathrm { k } + 2 } } { \frac { 5 } { \mathrm { k } ^ { 2 } - 4 } }$