Simplify Complex Rational Expressions
-$$\frac { \frac { x } { x - 2 } + 1 } { \frac { 3 } { x ^ { 2 } - 4 } + 1 }$$

Question

Quizplus · Accepted Answer

The correct answer is A because the numerator and denominator of the complex rational expression can be simplified as follows:$$\frac { \frac { x } { x - 2 } + 1 } { \frac { 3 } { x ^ { 2 } - 4 } + 1 } = \frac { \frac { x + x - 2 } { x - 2 } } { \frac { 3 } { ( x - 2 ) ( x + 2 ) } + 1 } = \frac { \frac { 2 x - 2 } { x - 2 } } { \frac { 3 + x + 2 } { ( x - 2 ) ( x + 2 ) } } = \frac { \frac { 2 ( x - 1 ) } { x - 2 } } { \frac { x + 5 } { ( x - 2 ) ( x + 2 ) } } = \frac { \frac { 2 ( x - 1 ) } { x - 2 } } { \frac { x + 5 } { ( x - 2 ) ( x + 2 ) } } = \frac { 2 ( x - 1 ) ( x + 2 ) } { ( x - 2 ) ( x + 5 ) } = \frac { 2 x + 4 } { x + 1 }$$

Simplify Complex Rational Expressions - xx−2+13x2−4+1\frac { \frac { x } { x - 2 } + 1 } { \frac { 3 } { x ^ { 2 } - 4 } + 1 }x2−43​+1x−2x​+1​

Simplify Complex Rational Expressions
- $\frac { \frac { x } { x - 2 } + 1 } { \frac { 3 } { x ^ { 2 } - 4 } + 1 }$